Dicas sobre ensino de logaritmos.

Logaritmos para muitos alunos é um conteúdo de difícil compreensão, provavelmente isso se deva ao fato de que não o utilizamos ele comumente no cotidiano. Talvez esse seja um dos motivos de não despertar muito interesse pelos alunos e se o professor simplesmente passar aquele monte de regras de potências e mudanças de base sem contextualizar nada o mais provável é que o aluno não se interesse muito pelo conteúdo. Sendo assim, este texto tem como objetivo dar algumas sugestões para que o professor possa estar incorporando à sua explanação para que o conteúdo não fique simplesmente jogado sem que o aluno veja utilidade alguma para aquilo.

Acredito que a primeira pergunta que deva vir à mente de alguém que está tendo o primeiro contato com logaritmos seja o porquê de terem o inventado. Sendo assim cabe aqui uma breve explanação sobre sua origem.

Os logaritmos foram criados por John Napier (1550-1617), natural da cidade de Edimburgo na Escócia. Ao contrário do que possa parecer, os logaritmos foram criados como um método de simplificar cálculos de multiplicação. Napier antes dos logaritmos criou um dispositivo de multiplicação conhecido hoje como “ossos de Napier”. Também foi quem desenvolveu as primeiras tábuas de logaritmos.

Para compreendermos como os logaritmos são utilizados para simplificar os cálculos temos que lembrar de suas propriedades. Duas das propriedades dos logaritmos são essas abaixo:

Sendo assim se você quiser encontrar o valor da multiplicação entre um valor “a” e um valor “b” basta somar o valor do logaritmo de “a” com o logaritmo de “b”, ambos em uma base “x” e o resultado será o logaritmo da multiplicação dos números. De forma análoga, partindo da segunda propriedade podemos resolver operações de divisão.

Geralmente as tabelas de logaritmos estão na base 10 (logaritmos decimais) como nessa tabela:

Utilizando esta tabela se quisermos, por exemplo, obter o valor da multiplicação 8x9 basta somar o logaritmo de 8 que vale 0,90309 com o logaritmo de 9 que vale 0,954243 obtendo o valor 1,857333 que corresponde ao logaritmo de 72 que é o resultado da multiplicação. Claro que para simplificar mais os cálculos geralmente usam-se tabelas com 4 casas decimais.

Sendo assim com uma tabela de logaritmos dá pra se fazer multiplicações e divisões serem reduzidas para operações de soma e subtração. Partindo dessa idéia surgiram as réguas de cálculo. Hoje em dia essa aplicação dos logaritmos não tem muita importância, pois podemos fazer cálculos muito mais rápido utilizando calculadoras digitais, no entanto os logaritmos continuaram a ter várias outras aplicações. Para mostrar algumas das várias aplicações dos logaritmos estaremos dando algumas sugestões que podem ser passadas de forma simples e que não são de difícil compreensão para o aluno de ensino médio.

O pH de uma solução.

Ao se falar sobre o potencial hidrogeniônico o professor de matemática pode fazer um trabalho interdisciplinar com o professor de química, mostrando uma das aplicações dos logaritmos e ao mesmo tempo fazendo um gancho com o conteúdo de química.

O potencial hidrogeniônico é uma grandeza que serve pra identificar se uma substância é ácida ou básica, ele foi introduzido em 1909 pelo bioquímico dinamarquês Søren Peter Lauritz Sørensen e é definido como sendo:

Nessa fórmula o  representa a concentração molar hidrogeniônica, dessa forma se uma solução apresentar um pH menor do que 7 ela é considerada ácida e se for maior que 7 ela é uma solução básica. Se o pH for 7 diz-se que a solução é neutra. Teoricamente o pH varia entre 0 e 14, porém esses não são os valores limites podendo, em alguns casos, ter valores além desses extremos.

Partindo pra um exemplo prático:

Temos que:

PROPRIEDADES DOS LOGARITMOS- VÍDEO-AULA

Tabela e tabuada de base 10 dos logaritimos de 1 a 500

Log10 (1) = 0
 Log10 (2) = 0,301029995663981
 Log10 (3) = 0,477121254719662
 Log10 (4) = 0,602059991327962
 Log10 (5) = 0,698970004336019
 Log10 (6) = 0,778151250383644
 Log10 (7) = 0,845098040014257
 Log10 (8) = 0,903089986991944
 Log10 (9) = 0,954242509439325
 Log10 (10) = 1
 Log10 (11) = 1,04139268515823
 Log10 (12) = 1,07918124604762
 Log10 (13) = 1,11394335230684
 Log10 (14) = 1,14612803567824
 Log10 (15) = 1,17609125905568
 Log10 (16) = 1,20411998265592
 Log10 (17) = 1,23044892137827
 Log10 (18) = 1,25527250510331
 Log10 (19) = 1,27875360095283
 Log10 (20) = 1,30102999566398
 Log10 (21) = 1,32221929473392
 Log10 (22) = 1,34242268082221
 Log10 (23) = 1,36172783601759
 Log10 (24) = 1,38021124171161
 Log10 (25) = 1,39794000867204
 Log10 (26) = 1,41497334797082
 Log10 (27) = 1,43136376415899
 Log10 (28) = 1,44715803134222
 Log10 (29) = 1,46239799789896
 Log10 (30) = 1,47712125471966
 Log10 (31) = 1,49136169383427
 Log10 (32) = 1,50514997831991
 Log10 (33) = 1,51851393987789
 Log10 (34) = 1,53147891704226
 Log10 (35) = 1,54406804435028
 Log10 (36) = 1,55630250076729
 Log10 (37) = 1,56820172406699
 Log10 (38) = 1,57978359661681
 Log10 (39) = 1,5910646070265
 Log10 (40) = 1,60205999132796
 Log10 (41) = 1,61278385671974
 Log10 (42) = 1,6232492903979
 Log10 (43) = 1,63346845557959
 Log10 (44) = 1,64345267648619
 Log10 (45) = 1,65321251377534
 Log10 (46) = 1,66275783168157
 Log10 (47) = 1,67209785793572
 Log10 (48) = 1,68124123737559
 Log10 (49) = 1,69019608002851
 Log10 (50) = 1,69897000433602
 Log10 (51) = 1,70757017609794
 Log10 (52) = 1,7160033436348
 Log10 (53) = 1,72427586960079
 Log10 (54) = 1,73239375982297
 Log10 (55) = 1,74036268949424
 Log10 (56) = 1,7481880270062
 Log10 (57) = 1,75587485567249
 Log10 (58) = 1,76342799356294
 Log10 (59) = 1,77085201164214
 Log10 (60) = 1,77815125038364
 Log10 (61) = 1,78532983501077
 Log10 (62) = 1,79239168949825
 Log10 (63) = 1,79934054945358
 Log10 (64) = 1,80617997398389
 Log10 (65) = 1,81291335664286
 Log10 (66) = 1,81954393554187
 Log10 (67) = 1,82607480270083
 Log10 (68) = 1,83250891270624
 Log10 (69) = 1,83884909073726
 Log10 (70) = 1,84509804001426
 Log10 (71) = 1,85125834871908
 Log10 (72) = 1,85733249643127
 Log10 (73) = 1,86332286012046
 Log10 (74) = 1,86923171973098
 Log10 (75) = 1,8750612633917
 Log10 (76) = 1,88081359228079
 Log10 (77) = 1,88649072517248
 Log10 (78) = 1,89209460269048
 Log10 (79) = 1,89762709129044
 Log10 (80) = 1,90308998699194
 Log10 (81) = 1,90848501887865
 Log10 (82) = 1,91381385238372
 Log10 (83) = 1,91907809237607
 Log10 (84) = 1,92427928606188
 Log10 (85) = 1,92941892571429
 Log10 (86) = 1,93449845124357
 Log10 (87) = 1,93951925261862
 Log10 (88) = 1,94448267215017
 Log10 (89) = 1,94939000664491
 Log10 (90) = 1,95424250943932
 Log10 (91) = 1,95904139232109
 Log10 (92) = 1,96378782734556
 Log10 (93) = 1,96848294855394
 Log10 (94) = 1,9731278535997
 Log10 (95) = 1,97772360528885
 Log10 (96) = 1,98227123303957
 Log10 (97) = 1,98677173426624
 Log10 (98) = 1,99122607569249
 Log10 (99) = 1,99563519459755
 Log10 (100) = 2
 Log10 (101) = 2,00432137378264
 Log10 (102) = 2,00860017176192
 Log10 (103) = 2,01283722470517
 Log10 (104) = 2,01703333929878
 Log10 (105) = 2,02118929906994
 Log10 (106) = 2,02530586526477
 Log10 (107) = 2,02938377768521
 Log10 (108) = 2,03342375548695
 Log10 (109) = 2,03742649794062
 Log10 (110) = 2,04139268515822
 Log10 (111) = 2,04532297878666
 Log10 (112) = 2,04921802267018
 Log10 (113) = 2,05307844348342
 Log10 (114) = 2,05690485133647
 Log10 (115) = 2,06069784035361
 Log10 (116) = 2,06445798922692
 Log10 (117) = 2,06818586174616
 Log10 (118) = 2,07188200730613
 Log10 (119) = 2,07554696139253
 Log10 (120) = 2,07918124604762
 Log10 (121) = 2,08278537031645
 Log10 (122) = 2,08635983067475
 Log10 (123) = 2,0899051114394
 Log10 (124) = 2,09342168516224
 Log10 (125) = 2,09691001300806
 Log10 (126) = 2,10037054511756
 Log10 (127) = 2,10380372095596
 Log10 (128) = 2,10720996964787
 Log10 (129) = 2,11058971029925
 Log10 (130) = 2,11394335230684
 Log10 (131) = 2,11727129565576
 Log10 (132) = 2,12057393120585
 Log10 (133) = 2,12385164096709
 Log10 (134) = 2,12710479836481
 Log10 (135) = 2,13033376849501
 Log10 (136) = 2,13353890837022
 Log10 (137) = 2,13672056715641
 Log10 (138) = 2,13987908640124
 Log10 (139) = 2,14301480025409
 Log10 (140) = 2,14612803567824
 Log10 (141) = 2,14921911265538
 Log10 (142) = 2,15228834438306
 Log10 (143) = 2,15533603746506
 Log10 (144) = 2,15836249209525
 Log10 (145) = 2,16136800223497
 Log10 (146) = 2,16435285578444
 Log10 (147) = 2,16731733474818
 Log10 (148) = 2,17026171539496
 Log10 (149) = 2,17318626841227
 Log10 (150) = 2,17609125905568
 Log10 (151) = 2,17897694729317
 Log10 (152) = 2,18184358794477
 Log10 (153) = 2,1846914308176
 Log10 (154) = 2,18752072083646
 Log10 (155) = 2,19033169817029
 Log10 (156) = 2,19312459835446
 Log10 (157) = 2,19589965240923
 Log10 (158) = 2,19865708695442
 Log10 (159) = 2,20139712432045
 Log10 (160) = 2,20411998265592
 Log10 (161) = 2,20682587603185
 Log10 (162) = 2,20951501454263
 Log10 (163) = 2,21218760440396
 Log10 (164) = 2,2148438480477
 Log10 (165) = 2,21748394421391
 Log10 (166) = 2,22010808804005
 Log10 (167) = 2,22271647114758
 Log10 (168) = 2,22530928172586
 Log10 (169) = 2,22788670461367
 Log10 (170) = 2,23044892137827
 Log10 (171) = 2,23299611039215
 Log10 (172) = 2,23552844690755
 Log10 (173) = 2,2380461031288
 Log10 (174) = 2,2405492482826
 Log10 (175) = 2,24303804868629
 Log10 (176) = 2,24551266781415
 Log10 (177) = 2,24797326636181
 Log10 (178) = 2,25042000230889
 Log10 (179) = 2,25285303097989
 Log10 (180) = 2,25527250510331
 Log10 (181) = 2,25767857486918
 Log10 (182) = 2,26007138798507
 Log10 (183) = 2,26245108973043
 Log10 (184) = 2,26481782300954
 Log10 (185) = 2,26717172840301
 Log10 (186) = 2,26951294421792
 Log10 (187) = 2,2718416065365
 Log10 (188) = 2,27415784926368
 Log10 (189) = 2,27646180417324
 Log10 (190) = 2,27875360095283
 Log10 (191) = 2,28103336724773
 Log10 (192) = 2,28330122870355
 Log10 (193) = 2,28555730900777
 Log10 (194) = 2,28780172993023
 Log10 (195) = 2,29003461136252
 Log10 (196) = 2,29225607135648
 Log10 (197) = 2,29446622616159
 Log10 (198) = 2,29666519026153
 Log10 (199) = 2,29885307640971
 Log10 (200) = 2,30102999566398
 Log10 (201) = 2,30319605742049
 Log10 (202) = 2,30535136944662
 Log10 (203) = 2,30749603791321
 Log10 (204) = 2,3096301674259
 Log10 (205) = 2,31175386105575
 Log10 (206) = 2,31386722036915
 Log10 (207) = 2,31597034545692
 Log10 (208) = 2,31806333496276
 Log10 (209) = 2,32014628611105
 Log10 (210) = 2,32221929473392
 Log10 (211) = 2,32428245529769
 Log10 (212) = 2,32633586092875
 Log10 (213) = 2,32837960343874
 Log10 (214) = 2,33041377334919
 Log10 (215) = 2,33243845991561
 Log10 (216) = 2,33445375115093
 Log10 (217) = 2,33645973384853
 Log10 (218) = 2,3384564936046
 Log10 (219) = 2,34044411484012
 Log10 (220) = 2,34242268082221
 Log10 (221) = 2,34439227368511
 Log10 (222) = 2,34635297445064
 Log10 (223) = 2,34830486304816
 Log10 (224) = 2,35024801833416
 Log10 (225) = 2,35218251811136
 Log10 (226) = 2,3541084391474
 Log10 (227) = 2,35602585719312
 Log10 (228) = 2,35793484700045
 Log10 (229) = 2,35983548233989
 Log10 (230) = 2,36172783601759
 Log10 (231) = 2,36361197989214
 Log10 (232) = 2,3654879848909
 Log10 (233) = 2,36735592102602
 Log10 (234) = 2,36921585741014
 Log10 (235) = 2,37106786227174
 Log10 (236) = 2,37291200297011
 Log10 (237) = 2,3747483460101
 Log10 (238) = 2,37657695705651
 Log10 (239) = 2,37839790094814
 Log10 (240) = 2,38021124171161
 Log10 (241) = 2,38201704257487
 Log10 (242) = 2,38381536598043
 Log10 (243) = 2,38560627359831
 Log10 (244) = 2,38738982633873
 Log10 (245) = 2,38916608436453
 Log10 (246) = 2,39093510710338
 Log10 (247) = 2,39269695325967
 Log10 (248) = 2,39445168082622
 Log10 (249) = 2,39619934709574
 Log10 (250) = 2,39794000867204
 Log10 (251) = 2,39967372148104
 Log10 (252) = 2,40140054078154
 Log10 (253) = 2,40312052117582
 Log10 (254) = 2,40483371661994
 Log10 (255) = 2,40654018043396
 Log10 (256) = 2,40823996531185
 Log10 (257) = 2,40993312333129
 Log10 (258) = 2,41161970596323
 Log10 (259) = 2,41329976408125
 Log10 (260) = 2,41497334797082
 Log10 (261) = 2,41664050733828
 Log10 (262) = 2,41830129131975
 Log10 (263) = 2,41995574848976
 Log10 (264) = 2,42160392686983
 Log10 (265) = 2,42324587393681
 Log10 (266) = 2,42488163663107
 Log10 (267) = 2,42651126136458
 Log10 (268) = 2,42813479402879
 Log10 (269) = 2,42975228000241
 Log10 (270) = 2,43136376415899
 Log10 (271) = 2,43296929087441
 Log10 (272) = 2,4345689040342
 Log10 (273) = 2,43616264704076
 Log10 (274) = 2,43775056282039
 Log10 (275) = 2,43933269383026
 Log10 (276) = 2,44090908206522
 Log10 (277) = 2,44247976906445
 Log10 (278) = 2,44404479591808
 Log10 (279) = 2,4456042032736
 Log10 (280) = 2,44715803134222
 Log10 (281) = 2,44870631990508
 Log10 (282) = 2,45024910831936
 Log10 (283) = 2,45178643552429
 Log10 (284) = 2,45331834004704
 Log10 (285) = 2,45484486000851
 Log10 (286) = 2,45636603312904
 Log10 (287) = 2,45788189673399
 Log10 (288) = 2,45939248775923
 Log10 (289) = 2,46089784275655
 Log10 (290) = 2,46239799789896
 Log10 (291) = 2,46389298898591
 Log10 (292) = 2,46538285144842
 Log10 (293) = 2,46686762035411
 Log10 (294) = 2,46834733041216
 Log10 (295) = 2,46982201597816
 Log10 (296) = 2,47129171105894
 Log10 (297) = 2,47275644931721
 Log10 (298) = 2,47421626407626
 Log10 (299) = 2,47567118832443
 Log10 (300) = 2,47712125471966
 Log10 (301) = 2,47856649559384
 Log10 (302) = 2,48000694295715
 Log10 (303) = 2,4814426285023
 Log10 (304) = 2,48287358360875
 Log10 (305) = 2,48429983934679
 Log10 (306) = 2,48572142648158
 Log10 (307) = 2,48713837547719
 Log10 (308) = 2,48855071650044
 Log10 (309) = 2,48995847942483
 Log10 (310) = 2,49136169383427
 Log10 (311) = 2,49276038902684
 Log10 (312) = 2,49415459401844
 Log10 (313) = 2,49554433754645
 Log10 (314) = 2,49692964807321
 Log10 (315) = 2,4983105537896
 Log10 (316) = 2,4996870826184
 Log10 (317) = 2,50105926221775
 Log10 (318) = 2,50242711998443
 Log10 (319) = 2,50379068305718
 Log10 (320) = 2,50514997831991
 Log10 (321) = 2,50650503240487
 Log10 (322) = 2,50785587169583
 Log10 (323) = 2,5092025223311
 Log10 (324) = 2,51054501020661
 Log10 (325) = 2,51188336097887
 Log10 (326) = 2,51321760006794
 Log10 (327) = 2,51454775266029
 Log10 (328) = 2,51587384371168
 Log10 (329) = 2,51719589794997
 Log10 (330) = 2,51851393987789
 Log10 (331) = 2,51982799377572
 Log10 (332) = 2,52113808370404
 Log10 (333) = 2,52244423350632
 Log10 (334) = 2,52374646681156
 Log10 (335) = 2,52504480703685
 Log10 (336) = 2,52633927738984
 Log10 (337) = 2,52762990087134
 Log10 (338) = 2,52891670027765
 Log10 (339) = 2,53019969820308
 Log10 (340) = 2,53147891704225
 Log10 (341) = 2,5327543789925
 Log10 (342) = 2,53402610605613
 Log10 (343) = 2,53529412004277
 Log10 (344) = 2,53655844257153
 Log10 (345) = 2,53781909507327
 Log10 (346) = 2,53907609879278
 Log10 (347) = 2,54032947479087
 Log10 (348) = 2,54157924394658
 Log10 (349) = 2,54282542695918
 Log10 (350) = 2,54406804435028
 Log10 (351) = 2,54530711646582
 Log10 (352) = 2,54654266347813
 Log10 (353) = 2,54777470538782
 Log10 (354) = 2,54900326202579
 Log10 (355) = 2,55022835305509
 Log10 (356) = 2,55144999797288
 Log10 (357) = 2,55266821611219
 Log10 (358) = 2,55388302664387
 Log10 (359) = 2,55509444857832
 Log10 (360) = 2,55630250076729
 Log10 (361) = 2,55750720190566
 Log10 (362) = 2,55870857053317
 Log10 (363) = 2,55990662503611
 Log10 (364) = 2,56110138364906
 Log10 (365) = 2,56229286445647
 Log10 (366) = 2,56348108539441
 Log10 (367) = 2,56466606425209
 Log10 (368) = 2,56584781867352
 Log10 (369) = 2,56702636615906
 Log10 (370) = 2,56820172406699
 Log10 (371) = 2,56937390961505
 Log10 (372) = 2,5705429398819
 Log10 (373) = 2,57170883180869
 Log10 (374) = 2,57287160220048
 Log10 (375) = 2,57403126772772
 Log10 (376) = 2,57518784492766
 Log10 (377) = 2,57634135020579
 Log10 (378) = 2,57749179983723
 Log10 (379) = 2,57863920996807
 Log10 (380) = 2,57978359661681
 Log10 (381) = 2,58092497567562
 Log10 (382) = 2,58206336291171
 Log10 (383) = 2,58319877396862
 Log10 (384) = 2,58433122436753
 Log10 (385) = 2,5854607295085
 Log10 (386) = 2,58658730467176
 Log10 (387) = 2,58771096501891
 Log10 (388) = 2,58883172559421
 Log10 (389) = 2,58994960132571
 Log10 (390) = 2,5910646070265
 Log10 (391) = 2,59217675739587
 Log10 (392) = 2,59328606702046
 Log10 (393) = 2,59439255037543
 Log10 (394) = 2,59549622182557
 Log10 (395) = 2,59659709562646
 Log10 (396) = 2,59769518592551
 Log10 (397) = 2,59879050676312
 Log10 (398) = 2,59988307207369
 Log10 (399) = 2,60097289568675
 Log10 (400) = 2,60205999132796
 Log10 (401) = 2,60314437262018
 Log10 (402) = 2,60422605308447
 Log10 (403) = 2,60530504614111
 Log10 (404) = 2,60638136511061
 Log10 (405) = 2,60745502321467
 Log10 (406) = 2,60852603357719
 Log10 (407) = 2,60959440922522
 Log10 (408) = 2,61066016308988
 Log10 (409) = 2,61172330800734
 Log10 (410) = 2,61278385671974
 Log10 (411) = 2,61384182187607
 Log10 (412) = 2,61489721603313
 Log10 (413) = 2,6159500516564
 Log10 (414) = 2,6170003411209
 Log10 (415) = 2,61804809671209
 Log10 (416) = 2,61909333062674
 Log10 (417) = 2,62013605497376
 Log10 (418) = 2,62117628177504
 Log10 (419) = 2,6222140229663
 Log10 (420) = 2,6232492903979
 Log10 (421) = 2,62428209583567
 Log10 (422) = 2,62531245096167
 Log10 (423) = 2,62634036737504
 Log10 (424) = 2,62736585659273
 Log10 (425) = 2,62838893005031
 Log10 (426) = 2,62940959910272
 Log10 (427) = 2,63042787502502
 Log10 (428) = 2,63144376901317
 Log10 (429) = 2,63245729218472
 Log10 (430) = 2,63346845557959
 Log10 (431) = 2,63447727016073
 Log10 (432) = 2,63548374681491
 Log10 (433) = 2,63648789635337
 Log10 (434) = 2,63748972951251
 Log10 (435) = 2,63848925695464
 Log10 (436) = 2,63948648926859
 Log10 (437) = 2,64048143697042
 Log10 (438) = 2,6414741105041
 Log10 (439) = 2,64246452024212
 Log10 (440) = 2,64345267648619
 Log10 (441) = 2,64443858946784
 Log10 (442) = 2,64542226934909
 Log10 (443) = 2,64640372622307
 Log10 (444) = 2,64738297011462
 Log10 (445) = 2,64836001098093
 Log10 (446) = 2,64933485871214
 Log10 (447) = 2,65030752313194
 Log10 (448) = 2,65127801399814
 Log10 (449) = 2,65224634100332
 Log10 (450) = 2,65321251377534
 Log10 (451) = 2,65417654187796
 Log10 (452) = 2,65513843481138
 Log10 (453) = 2,65609820201283
 Log10 (454) = 2,6570558528571
 Log10 (455) = 2,65801139665711
 Log10 (456) = 2,65896484266443
 Log10 (457) = 2,65991620006985
 Log10 (458) = 2,66086547800387
 Log10 (459) = 2,66181268553726
 Log10 (460) = 2,66275783168157
 Log10 (461) = 2,66370092538965
 Log10 (462) = 2,66464197555613
 Log10 (463) = 2,66558099101795
 Log10 (464) = 2,66651798055488
 Log10 (465) = 2,66745295288995
 Log10 (466) = 2,66838591669
 Log10 (467) = 2,66931688056611
 Log10 (468) = 2,67024585307412
 Log10 (469) = 2,67117284271508
 Log10 (470) = 2,67209785793572
 Log10 (471) = 2,6730209071289
 Log10 (472) = 2,67394199863409
 Log10 (473) = 2,67486114073781
 Log10 (474) = 2,67577834167409
 Log10 (475) = 2,67669360962487
 Log10 (476) = 2,67760695272049
 Log10 (477) = 2,67851837904011
 Log10 (478) = 2,67942789661212
 Log10 (479) = 2,68033551341456
 Log10 (480) = 2,68124123737559
 Log10 (481) = 2,68214507637383
 Log10 (482) = 2,68304703823885
 Log10 (483) = 2,68394713075151
 Log10 (484) = 2,68484536164441
 Log10 (485) = 2,68574173860226
 Log10 (486) = 2,68663626926229
 Log10 (487) = 2,68752896121463
 Log10 (488) = 2,68841982200271
 Log10 (489) = 2,68930885912362
 Log10 (490) = 2,69019608002851
 Log10 (491) = 2,69108149212297
 Log10 (492) = 2,69196510276736
 Log10 (493) = 2,69284691927723
 Log10 (494) = 2,69372694892365
 Log10 (495) = 2,69460519893357
 Log10 (496) = 2,6954816764902
 Log10 (497) = 2,69635638873333
 Log10 (498) = 2,69722934275972
 Log10 (499) = 2,69810054562339
 Log10 (500) = 2,69897000433602Log10 (1) = 0
 Log10 (2) = 0,301029995663981
 Log10 (3) = 0,477121254719662
 Log10 (4) = 0,602059991327962
 Log10 (5) = 0,698970004336019
 Log10 (6) = 0,778151250383644
 Log10 (7) = 0,845098040014257
 Log10 (8) = 0,903089986991944
 Log10 (9) = 0,954242509439325
 Log10 (10) = 1
 Log10 (11) = 1,04139268515823
 Log10 (12) = 1,07918124604762
 Log10 (13) = 1,11394335230684
 Log10 (14) = 1,14612803567824
 Log10 (15) = 1,17609125905568
 Log10 (16) = 1,20411998265592
 Log10 (17) = 1,23044892137827
 Log10 (18) = 1,25527250510331
 Log10 (19) = 1,27875360095283
 Log10 (20) = 1,30102999566398
 Log10 (21) = 1,32221929473392
 Log10 (22) = 1,34242268082221
 Log10 (23) = 1,36172783601759
 Log10 (24) = 1,38021124171161
 Log10 (25) = 1,39794000867204
 Log10 (26) = 1,41497334797082
 Log10 (27) = 1,43136376415899
 Log10 (28) = 1,44715803134222
 Log10 (29) = 1,46239799789896
 Log10 (30) = 1,47712125471966
 Log10 (31) = 1,49136169383427
 Log10 (32) = 1,50514997831991
 Log10 (33) = 1,51851393987789
 Log10 (34) = 1,53147891704226
 Log10 (35) = 1,54406804435028
 Log10 (36) = 1,55630250076729
 Log10 (37) = 1,56820172406699
 Log10 (38) = 1,57978359661681
 Log10 (39) = 1,5910646070265
 Log10 (40) = 1,60205999132796
 Log10 (41) = 1,61278385671974
 Log10 (42) = 1,6232492903979
 Log10 (43) = 1,63346845557959
 Log10 (44) = 1,64345267648619
 Log10 (45) = 1,65321251377534
 Log10 (46) = 1,66275783168157
 Log10 (47) = 1,67209785793572
 Log10 (48) = 1,68124123737559
 Log10 (49) = 1,69019608002851
 Log10 (50) = 1,69897000433602
 Log10 (51) = 1,70757017609794
 Log10 (52) = 1,7160033436348
 Log10 (53) = 1,72427586960079
 Log10 (54) = 1,73239375982297
 Log10 (55) = 1,74036268949424
 Log10 (56) = 1,7481880270062
 Log10 (57) = 1,75587485567249
 Log10 (58) = 1,76342799356294
 Log10 (59) = 1,77085201164214
 Log10 (60) = 1,77815125038364
 Log10 (61) = 1,78532983501077
 Log10 (62) = 1,79239168949825
 Log10 (63) = 1,79934054945358
 Log10 (64) = 1,80617997398389
 Log10 (65) = 1,81291335664286
 Log10 (66) = 1,81954393554187
 Log10 (67) = 1,82607480270083
 Log10 (68) = 1,83250891270624
 Log10 (69) = 1,83884909073726
 Log10 (70) = 1,84509804001426
 Log10 (71) = 1,85125834871908
 Log10 (72) = 1,85733249643127
 Log10 (73) = 1,86332286012046
 Log10 (74) = 1,86923171973098
 Log10 (75) = 1,8750612633917
 Log10 (76) = 1,88081359228079
 Log10 (77) = 1,88649072517248
 Log10 (78) = 1,89209460269048
 Log10 (79) = 1,89762709129044
 Log10 (80) = 1,90308998699194
 Log10 (81) = 1,90848501887865
 Log10 (82) = 1,91381385238372
 Log10 (83) = 1,91907809237607
 Log10 (84) = 1,92427928606188
 Log10 (85) = 1,92941892571429
 Log10 (86) = 1,93449845124357
 Log10 (87) = 1,93951925261862
 Log10 (88) = 1,94448267215017
 Log10 (89) = 1,94939000664491
 Log10 (90) = 1,95424250943932
 Log10 (91) = 1,95904139232109
 Log10 (92) = 1,96378782734556
 Log10 (93) = 1,96848294855394
 Log10 (94) = 1,9731278535997
 Log10 (95) = 1,97772360528885
 Log10 (96) = 1,98227123303957
 Log10 (97) = 1,98677173426624
 Log10 (98) = 1,99122607569249
 Log10 (99) = 1,99563519459755
 Log10 (100) = 2
 Log10 (101) = 2,00432137378264
 Log10 (102) = 2,00860017176192
 Log10 (103) = 2,01283722470517
 Log10 (104) = 2,01703333929878
 Log10 (105) = 2,02118929906994
 Log10 (106) = 2,02530586526477
 Log10 (107) = 2,02938377768521
 Log10 (108) = 2,03342375548695
 Log10 (109) = 2,03742649794062
 Log10 (110) = 2,04139268515822
 Log10 (111) = 2,04532297878666
 Log10 (112) = 2,04921802267018
 Log10 (113) = 2,05307844348342
 Log10 (114) = 2,05690485133647
 Log10 (115) = 2,06069784035361
 Log10 (116) = 2,06445798922692
 Log10 (117) = 2,06818586174616
 Log10 (118) = 2,07188200730613
 Log10 (119) = 2,07554696139253
 Log10 (120) = 2,07918124604762
 Log10 (121) = 2,08278537031645
 Log10 (122) = 2,08635983067475
 Log10 (123) = 2,0899051114394
 Log10 (124) = 2,09342168516224
 Log10 (125) = 2,09691001300806
 Log10 (126) = 2,10037054511756
 Log10 (127) = 2,10380372095596
 Log10 (128) = 2,10720996964787
 Log10 (129) = 2,11058971029925
 Log10 (130) = 2,11394335230684
 Log10 (131) = 2,11727129565576
 Log10 (132) = 2,12057393120585
 Log10 (133) = 2,12385164096709
 Log10 (134) = 2,12710479836481
 Log10 (135) = 2,13033376849501
 Log10 (136) = 2,13353890837022
 Log10 (137) = 2,13672056715641
 Log10 (138) = 2,13987908640124
 Log10 (139) = 2,14301480025409
 Log10 (140) = 2,14612803567824
 Log10 (141) = 2,14921911265538
 Log10 (142) = 2,15228834438306
 Log10 (143) = 2,15533603746506
 Log10 (144) = 2,15836249209525
 Log10 (145) = 2,16136800223497
 Log10 (146) = 2,16435285578444
 Log10 (147) = 2,16731733474818
 Log10 (148) = 2,17026171539496
 Log10 (149) = 2,17318626841227
 Log10 (150) = 2,17609125905568
 Log10 (151) = 2,17897694729317
 Log10 (152) = 2,18184358794477
 Log10 (153) = 2,1846914308176
 Log10 (154) = 2,18752072083646
 Log10 (155) = 2,19033169817029
 Log10 (156) = 2,19312459835446
 Log10 (157) = 2,19589965240923
 Log10 (158) = 2,19865708695442
 Log10 (159) = 2,20139712432045
 Log10 (160) = 2,20411998265592
 Log10 (161) = 2,20682587603185
 Log10 (162) = 2,20951501454263
 Log10 (163) = 2,21218760440396
 Log10 (164) = 2,2148438480477
 Log10 (165) = 2,21748394421391
 Log10 (166) = 2,22010808804005
 Log10 (167) = 2,22271647114758
 Log10 (168) = 2,22530928172586
 Log10 (169) = 2,22788670461367
 Log10 (170) = 2,23044892137827
 Log10 (171) = 2,23299611039215
 Log10 (172) = 2,23552844690755
 Log10 (173) = 2,2380461031288
 Log10 (174) = 2,2405492482826
 Log10 (175) = 2,24303804868629
 Log10 (176) = 2,24551266781415
 Log10 (177) = 2,24797326636181
 Log10 (178) = 2,25042000230889
 Log10 (179) = 2,25285303097989
 Log10 (180) = 2,25527250510331
 Log10 (181) = 2,25767857486918
 Log10 (182) = 2,26007138798507
 Log10 (183) = 2,26245108973043
 Log10 (184) = 2,26481782300954
 Log10 (185) = 2,26717172840301
 Log10 (186) = 2,26951294421792
 Log10 (187) = 2,2718416065365
 Log10 (188) = 2,27415784926368
 Log10 (189) = 2,27646180417324
 Log10 (190) = 2,27875360095283
 Log10 (191) = 2,28103336724773
 Log10 (192) = 2,28330122870355
 Log10 (193) = 2,28555730900777
 Log10 (194) = 2,28780172993023
 Log10 (195) = 2,29003461136252
 Log10 (196) = 2,29225607135648
 Log10 (197) = 2,29446622616159
 Log10 (198) = 2,29666519026153
 Log10 (199) = 2,29885307640971
 Log10 (200) = 2,30102999566398
 Log10 (201) = 2,30319605742049
 Log10 (202) = 2,30535136944662
 Log10 (203) = 2,30749603791321
 Log10 (204) = 2,3096301674259
 Log10 (205) = 2,31175386105575
 Log10 (206) = 2,31386722036915
 Log10 (207) = 2,31597034545692
 Log10 (208) = 2,31806333496276
 Log10 (209) = 2,32014628611105
 Log10 (210) = 2,32221929473392
 Log10 (211) = 2,32428245529769
 Log10 (212) = 2,32633586092875
 Log10 (213) = 2,32837960343874
 Log10 (214) = 2,33041377334919
 Log10 (215) = 2,33243845991561
 Log10 (216) = 2,33445375115093
 Log10 (217) = 2,33645973384853
 Log10 (218) = 2,3384564936046
 Log10 (219) = 2,34044411484012
 Log10 (220) = 2,34242268082221
 Log10 (221) = 2,34439227368511
 Log10 (222) = 2,34635297445064
 Log10 (223) = 2,34830486304816
 Log10 (224) = 2,35024801833416
 Log10 (225) = 2,35218251811136
 Log10 (226) = 2,3541084391474
 Log10 (227) = 2,35602585719312
 Log10 (228) = 2,35793484700045
 Log10 (229) = 2,35983548233989
 Log10 (230) = 2,36172783601759
 Log10 (231) = 2,36361197989214
 Log10 (232) = 2,3654879848909
 Log10 (233) = 2,36735592102602
 Log10 (234) = 2,36921585741014
 Log10 (235) = 2,37106786227174
 Log10 (236) = 2,37291200297011
 Log10 (237) = 2,3747483460101
 Log10 (238) = 2,37657695705651
 Log10 (239) = 2,37839790094814
 Log10 (240) = 2,38021124171161
 Log10 (241) = 2,38201704257487
 Log10 (242) = 2,38381536598043
 Log10 (243) = 2,38560627359831
 Log10 (244) = 2,38738982633873
 Log10 (245) = 2,38916608436453
 Log10 (246) = 2,39093510710338
 Log10 (247) = 2,39269695325967
 Log10 (248) = 2,39445168082622
 Log10 (249) = 2,39619934709574
 Log10 (250) = 2,39794000867204
 Log10 (251) = 2,39967372148104
 Log10 (252) = 2,40140054078154
 Log10 (253) = 2,40312052117582
 Log10 (254) = 2,40483371661994
 Log10 (255) = 2,40654018043396
 Log10 (256) = 2,40823996531185
 Log10 (257) = 2,40993312333129
 Log10 (258) = 2,41161970596323
 Log10 (259) = 2,41329976408125
 Log10 (260) = 2,41497334797082
 Log10 (261) = 2,41664050733828
 Log10 (262) = 2,41830129131975
 Log10 (263) = 2,41995574848976
 Log10 (264) = 2,42160392686983
 Log10 (265) = 2,42324587393681
 Log10 (266) = 2,42488163663107
 Log10 (267) = 2,42651126136458
 Log10 (268) = 2,42813479402879
 Log10 (269) = 2,42975228000241
 Log10 (270) = 2,43136376415899
 Log10 (271) = 2,43296929087441
 Log10 (272) = 2,4345689040342
 Log10 (273) = 2,43616264704076
 Log10 (274) = 2,43775056282039
 Log10 (275) = 2,43933269383026
 Log10 (276) = 2,44090908206522
 Log10 (277) = 2,44247976906445
 Log10 (278) = 2,44404479591808
 Log10 (279) = 2,4456042032736
 Log10 (280) = 2,44715803134222
 Log10 (281) = 2,44870631990508
 Log10 (282) = 2,45024910831936
 Log10 (283) = 2,45178643552429
 Log10 (284) = 2,45331834004704
 Log10 (285) = 2,45484486000851
 Log10 (286) = 2,45636603312904
 Log10 (287) = 2,45788189673399
 Log10 (288) = 2,45939248775923
 Log10 (289) = 2,46089784275655
 Log10 (290) = 2,46239799789896
 Log10 (291) = 2,46389298898591
 Log10 (292) = 2,46538285144842
 Log10 (293) = 2,46686762035411
 Log10 (294) = 2,46834733041216
 Log10 (295) = 2,46982201597816
 Log10 (296) = 2,47129171105894
 Log10 (297) = 2,47275644931721
 Log10 (298) = 2,47421626407626
 Log10 (299) = 2,47567118832443
 Log10 (300) = 2,47712125471966
 Log10 (301) = 2,47856649559384
 Log10 (302) = 2,48000694295715
 Log10 (303) = 2,4814426285023
 Log10 (304) = 2,48287358360875
 Log10 (305) = 2,48429983934679
 Log10 (306) = 2,48572142648158
 Log10 (307) = 2,48713837547719
 Log10 (308) = 2,48855071650044
 Log10 (309) = 2,48995847942483
 Log10 (310) = 2,49136169383427
 Log10 (311) = 2,49276038902684
 Log10 (312) = 2,49415459401844
 Log10 (313) = 2,49554433754645
 Log10 (314) = 2,49692964807321
 Log10 (315) = 2,4983105537896
 Log10 (316) = 2,4996870826184
 Log10 (317) = 2,50105926221775
 Log10 (318) = 2,50242711998443
 Log10 (319) = 2,50379068305718
 Log10 (320) = 2,50514997831991
 Log10 (321) = 2,50650503240487
 Log10 (322) = 2,50785587169583
 Log10 (323) = 2,5092025223311
 Log10 (324) = 2,51054501020661
 Log10 (325) = 2,51188336097887
 Log10 (326) = 2,51321760006794
 Log10 (327) = 2,51454775266029
 Log10 (328) = 2,51587384371168
 Log10 (329) = 2,51719589794997
 Log10 (330) = 2,51851393987789
 Log10 (331) = 2,51982799377572
 Log10 (332) = 2,52113808370404
 Log10 (333) = 2,52244423350632
 Log10 (334) = 2,52374646681156
 Log10 (335) = 2,52504480703685
 Log10 (336) = 2,52633927738984
 Log10 (337) = 2,52762990087134
 Log10 (338) = 2,52891670027765
 Log10 (339) = 2,53019969820308
 Log10 (340) = 2,53147891704225
 Log10 (341) = 2,5327543789925
 Log10 (342) = 2,53402610605613
 Log10 (343) = 2,53529412004277
 Log10 (344) = 2,53655844257153
 Log10 (345) = 2,53781909507327
 Log10 (346) = 2,53907609879278
 Log10 (347) = 2,54032947479087
 Log10 (348) = 2,54157924394658
 Log10 (349) = 2,54282542695918
 Log10 (350) = 2,54406804435028
 Log10 (351) = 2,54530711646582
 Log10 (352) = 2,54654266347813
 Log10 (353) = 2,54777470538782
 Log10 (354) = 2,54900326202579
 Log10 (355) = 2,55022835305509
 Log10 (356) = 2,55144999797288
 Log10 (357) = 2,55266821611219
 Log10 (358) = 2,55388302664387
 Log10 (359) = 2,55509444857832
 Log10 (360) = 2,55630250076729
 Log10 (361) = 2,55750720190566
 Log10 (362) = 2,55870857053317
 Log10 (363) = 2,55990662503611
 Log10 (364) = 2,56110138364906
 Log10 (365) = 2,56229286445647
 Log10 (366) = 2,56348108539441
 Log10 (367) = 2,56466606425209
 Log10 (368) = 2,56584781867352
 Log10 (369) = 2,56702636615906
 Log10 (370) = 2,56820172406699
 Log10 (371) = 2,56937390961505
 Log10 (372) = 2,5705429398819
 Log10 (373) = 2,57170883180869
 Log10 (374) = 2,57287160220048
 Log10 (375) = 2,57403126772772
 Log10 (376) = 2,57518784492766
 Log10 (377) = 2,57634135020579
 Log10 (378) = 2,57749179983723
 Log10 (379) = 2,57863920996807
 Log10 (380) = 2,57978359661681
 Log10 (381) = 2,58092497567562
 Log10 (382) = 2,58206336291171
 Log10 (383) = 2,58319877396862
 Log10 (384) = 2,58433122436753
 Log10 (385) = 2,5854607295085
 Log10 (386) = 2,58658730467176
 Log10 (387) = 2,58771096501891
 Log10 (388) = 2,58883172559421
 Log10 (389) = 2,58994960132571
 Log10 (390) = 2,5910646070265
 Log10 (391) = 2,59217675739587
 Log10 (392) = 2,59328606702046
 Log10 (393) = 2,59439255037543
 Log10 (394) = 2,59549622182557
 Log10 (395) = 2,59659709562646
 Log10 (396) = 2,59769518592551
 Log10 (397) = 2,59879050676312
 Log10 (398) = 2,59988307207369
 Log10 (399) = 2,60097289568675
 Log10 (400) = 2,60205999132796
 Log10 (401) = 2,60314437262018
 Log10 (402) = 2,60422605308447
 Log10 (403) = 2,60530504614111
 Log10 (404) = 2,60638136511061
 Log10 (405) = 2,60745502321467
 Log10 (406) = 2,60852603357719
 Log10 (407) = 2,60959440922522
 Log10 (408) = 2,61066016308988
 Log10 (409) = 2,61172330800734
 Log10 (410) = 2,61278385671974
 Log10 (411) = 2,61384182187607
 Log10 (412) = 2,61489721603313
 Log10 (413) = 2,6159500516564
 Log10 (414) = 2,6170003411209
 Log10 (415) = 2,61804809671209
 Log10 (416) = 2,61909333062674
 Log10 (417) = 2,62013605497376
 Log10 (418) = 2,62117628177504
 Log10 (419) = 2,6222140229663
 Log10 (420) = 2,6232492903979
 Log10 (421) = 2,62428209583567
 Log10 (422) = 2,62531245096167
 Log10 (423) = 2,62634036737504
 Log10 (424) = 2,62736585659273
 Log10 (425) = 2,62838893005031
 Log10 (426) = 2,62940959910272
 Log10 (427) = 2,63042787502502
 Log10 (428) = 2,63144376901317
 Log10 (429) = 2,63245729218472
 Log10 (430) = 2,63346845557959
 Log10 (431) = 2,63447727016073
 Log10 (432) = 2,63548374681491
 Log10 (433) = 2,63648789635337
 Log10 (434) = 2,63748972951251
 Log10 (435) = 2,63848925695464
 Log10 (436) = 2,63948648926859
 Log10 (437) = 2,64048143697042
 Log10 (438) = 2,6414741105041
 Log10 (439) = 2,64246452024212
 Log10 (440) = 2,64345267648619
 Log10 (441) = 2,64443858946784
 Log10 (442) = 2,64542226934909
 Log10 (443) = 2,64640372622307
 Log10 (444) = 2,64738297011462
 Log10 (445) = 2,64836001098093
 Log10 (446) = 2,64933485871214
 Log10 (447) = 2,65030752313194
 Log10 (448) = 2,65127801399814
 Log10 (449) = 2,65224634100332
 Log10 (450) = 2,65321251377534
 Log10 (451) = 2,65417654187796
 Log10 (452) = 2,65513843481138
 Log10 (453) = 2,65609820201283
 Log10 (454) = 2,6570558528571
 Log10 (455) = 2,65801139665711
 Log10 (456) = 2,65896484266443
 Log10 (457) = 2,65991620006985
 Log10 (458) = 2,66086547800387
 Log10 (459) = 2,66181268553726
 Log10 (460) = 2,66275783168157
 Log10 (461) = 2,66370092538965
 Log10 (462) = 2,66464197555613
 Log10 (463) = 2,66558099101795
 Log10 (464) = 2,66651798055488
 Log10 (465) = 2,66745295288995
 Log10 (466) = 2,66838591669
 Log10 (467) = 2,66931688056611
 Log10 (468) = 2,67024585307412
 Log10 (469) = 2,67117284271508
 Log10 (470) = 2,67209785793572
 Log10 (471) = 2,6730209071289
 Log10 (472) = 2,67394199863409
 Log10 (473) = 2,67486114073781
 Log10 (474) = 2,67577834167409
 Log10 (475) = 2,67669360962487
 Log10 (476) = 2,67760695272049
 Log10 (477) = 2,67851837904011
 Log10 (478) = 2,67942789661212
 Log10 (479) = 2,68033551341456
 Log10 (480) = 2,68124123737559
 Log10 (481) = 2,68214507637383
 Log10 (482) = 2,68304703823885
 Log10 (483) = 2,68394713075151
 Log10 (484) = 2,68484536164441
 Log10 (485) = 2,68574173860226
 Log10 (486) = 2,68663626926229
 Log10 (487) = 2,68752896121463
 Log10 (488) = 2,68841982200271
 Log10 (489) = 2,68930885912362
 Log10 (490) = 2,69019608002851
 Log10 (491) = 2,69108149212297
 Log10 (492) = 2,69196510276736
 Log10 (493) = 2,69284691927723
 Log10 (494) = 2,69372694892365
 Log10 (495) = 2,69460519893357
 Log10 (496) = 2,6954816764902
 Log10 (497) = 2,69635638873333
 Log10 (498) = 2,69722934275972
 Log10 (499) = 2,69810054562339
 Log10 (500) = 2,69897000433602

Tabela e tabuada de base 10 dos logaritmos de 1 a 500

Log10 (1) = 0
 Log10 (2) = 0,301029995663981
 Log10 (3) = 0,477121254719662
 Log10 (4) = 0,602059991327962
 Log10 (5) = 0,698970004336019
 Log10 (6) = 0,778151250383644
 Log10 (7) = 0,845098040014257
 Log10 (8) = 0,903089986991944
 Log10 (9) = 0,954242509439325
 Log10 (10) = 1
 Log10 (11) = 1,04139268515823
 Log10 (12) = 1,07918124604762
 Log10 (13) = 1,11394335230684
 Log10 (14) = 1,14612803567824
 Log10 (15) = 1,17609125905568
 Log10 (16) = 1,20411998265592
 Log10 (17) = 1,23044892137827
 Log10 (18) = 1,25527250510331
 Log10 (19) = 1,27875360095283
 Log10 (20) = 1,30102999566398
 Log10 (21) = 1,32221929473392
 Log10 (22) = 1,34242268082221
 Log10 (23) = 1,36172783601759
 Log10 (24) = 1,38021124171161
 Log10 (25) = 1,39794000867204
 Log10 (26) = 1,41497334797082
 Log10 (27) = 1,43136376415899
 Log10 (28) = 1,44715803134222
 Log10 (29) = 1,46239799789896
 Log10 (30) = 1,47712125471966
 Log10 (31) = 1,49136169383427
 Log10 (32) = 1,50514997831991
 Log10 (33) = 1,51851393987789
 Log10 (34) = 1,53147891704226
 Log10 (35) = 1,54406804435028
 Log10 (36) = 1,55630250076729
 Log10 (37) = 1,56820172406699
 Log10 (38) = 1,57978359661681
 Log10 (39) = 1,5910646070265
 Log10 (40) = 1,60205999132796
 Log10 (41) = 1,61278385671974
 Log10 (42) = 1,6232492903979
 Log10 (43) = 1,63346845557959
 Log10 (44) = 1,64345267648619
 Log10 (45) = 1,65321251377534
 Log10 (46) = 1,66275783168157
 Log10 (47) = 1,67209785793572
 Log10 (48) = 1,68124123737559
 Log10 (49) = 1,69019608002851
 Log10 (50) = 1,69897000433602
 Log10 (51) = 1,70757017609794
 Log10 (52) = 1,7160033436348
 Log10 (53) = 1,72427586960079
 Log10 (54) = 1,73239375982297
 Log10 (55) = 1,74036268949424
 Log10 (56) = 1,7481880270062
 Log10 (57) = 1,75587485567249
 Log10 (58) = 1,76342799356294
 Log10 (59) = 1,77085201164214
 Log10 (60) = 1,77815125038364
 Log10 (61) = 1,78532983501077
 Log10 (62) = 1,79239168949825
 Log10 (63) = 1,79934054945358
 Log10 (64) = 1,80617997398389
 Log10 (65) = 1,81291335664286
 Log10 (66) = 1,81954393554187
 Log10 (67) = 1,82607480270083
 Log10 (68) = 1,83250891270624
 Log10 (69) = 1,83884909073726
 Log10 (70) = 1,84509804001426
 Log10 (71) = 1,85125834871908
 Log10 (72) = 1,85733249643127
 Log10 (73) = 1,86332286012046
 Log10 (74) = 1,86923171973098
 Log10 (75) = 1,8750612633917
 Log10 (76) = 1,88081359228079
 Log10 (77) = 1,88649072517248
 Log10 (78) = 1,89209460269048
 Log10 (79) = 1,89762709129044
 Log10 (80) = 1,90308998699194
 Log10 (81) = 1,90848501887865
 Log10 (82) = 1,91381385238372
 Log10 (83) = 1,91907809237607
 Log10 (84) = 1,92427928606188
 Log10 (85) = 1,92941892571429
 Log10 (86) = 1,93449845124357
 Log10 (87) = 1,93951925261862
 Log10 (88) = 1,94448267215017
 Log10 (89) = 1,94939000664491
 Log10 (90) = 1,95424250943932
 Log10 (91) = 1,95904139232109
 Log10 (92) = 1,96378782734556
 Log10 (93) = 1,96848294855394
 Log10 (94) = 1,9731278535997
 Log10 (95) = 1,97772360528885
 Log10 (96) = 1,98227123303957
 Log10 (97) = 1,98677173426624
 Log10 (98) = 1,99122607569249
 Log10 (99) = 1,99563519459755
 Log10 (100) = 2
 Log10 (101) = 2,00432137378264
 Log10 (102) = 2,00860017176192
 Log10 (103) = 2,01283722470517
 Log10 (104) = 2,01703333929878
 Log10 (105) = 2,02118929906994
 Log10 (106) = 2,02530586526477
 Log10 (107) = 2,02938377768521
 Log10 (108) = 2,03342375548695
 Log10 (109) = 2,03742649794062
 Log10 (110) = 2,04139268515822
 Log10 (111) = 2,04532297878666
 Log10 (112) = 2,04921802267018
 Log10 (113) = 2,05307844348342
 Log10 (114) = 2,05690485133647
 Log10 (115) = 2,06069784035361
 Log10 (116) = 2,06445798922692
 Log10 (117) = 2,06818586174616
 Log10 (118) = 2,07188200730613
 Log10 (119) = 2,07554696139253
 Log10 (120) = 2,07918124604762
 Log10 (121) = 2,08278537031645
 Log10 (122) = 2,08635983067475
 Log10 (123) = 2,0899051114394
 Log10 (124) = 2,09342168516224
 Log10 (125) = 2,09691001300806
 Log10 (126) = 2,10037054511756
 Log10 (127) = 2,10380372095596
 Log10 (128) = 2,10720996964787
 Log10 (129) = 2,11058971029925
 Log10 (130) = 2,11394335230684
 Log10 (131) = 2,11727129565576
 Log10 (132) = 2,12057393120585
 Log10 (133) = 2,12385164096709
 Log10 (134) = 2,12710479836481
 Log10 (135) = 2,13033376849501
 Log10 (136) = 2,13353890837022
 Log10 (137) = 2,13672056715641
 Log10 (138) = 2,13987908640124
 Log10 (139) = 2,14301480025409
 Log10 (140) = 2,14612803567824
 Log10 (141) = 2,14921911265538
 Log10 (142) = 2,15228834438306
 Log10 (143) = 2,15533603746506
 Log10 (144) = 2,15836249209525
 Log10 (145) = 2,16136800223497
 Log10 (146) = 2,16435285578444
 Log10 (147) = 2,16731733474818
 Log10 (148) = 2,17026171539496
 Log10 (149) = 2,17318626841227
 Log10 (150) = 2,17609125905568
 Log10 (151) = 2,17897694729317
 Log10 (152) = 2,18184358794477
 Log10 (153) = 2,1846914308176
 Log10 (154) = 2,18752072083646
 Log10 (155) = 2,19033169817029
 Log10 (156) = 2,19312459835446
 Log10 (157) = 2,19589965240923
 Log10 (158) = 2,19865708695442
 Log10 (159) = 2,20139712432045
 Log10 (160) = 2,20411998265592
 Log10 (161) = 2,20682587603185
 Log10 (162) = 2,20951501454263
 Log10 (163) = 2,21218760440396
 Log10 (164) = 2,2148438480477
 Log10 (165) = 2,21748394421391
 Log10 (166) = 2,22010808804005
 Log10 (167) = 2,22271647114758
 Log10 (168) = 2,22530928172586
 Log10 (169) = 2,22788670461367
 Log10 (170) = 2,23044892137827
 Log10 (171) = 2,23299611039215
 Log10 (172) = 2,23552844690755
 Log10 (173) = 2,2380461031288
 Log10 (174) = 2,2405492482826
 Log10 (175) = 2,24303804868629
 Log10 (176) = 2,24551266781415
 Log10 (177) = 2,24797326636181
 Log10 (178) = 2,25042000230889
 Log10 (179) = 2,25285303097989
 Log10 (180) = 2,25527250510331
 Log10 (181) = 2,25767857486918
 Log10 (182) = 2,26007138798507
 Log10 (183) = 2,26245108973043
 Log10 (184) = 2,26481782300954
 Log10 (185) = 2,26717172840301
 Log10 (186) = 2,26951294421792
 Log10 (187) = 2,2718416065365
 Log10 (188) = 2,27415784926368
 Log10 (189) = 2,27646180417324
 Log10 (190) = 2,27875360095283
 Log10 (191) = 2,28103336724773
 Log10 (192) = 2,28330122870355
 Log10 (193) = 2,28555730900777
 Log10 (194) = 2,28780172993023
 Log10 (195) = 2,29003461136252
 Log10 (196) = 2,29225607135648
 Log10 (197) = 2,29446622616159
 Log10 (198) = 2,29666519026153
 Log10 (199) = 2,29885307640971
 Log10 (200) = 2,30102999566398
 Log10 (201) = 2,30319605742049
 Log10 (202) = 2,30535136944662
 Log10 (203) = 2,30749603791321
 Log10 (204) = 2,3096301674259
 Log10 (205) = 2,31175386105575
 Log10 (206) = 2,31386722036915
 Log10 (207) = 2,31597034545692
 Log10 (208) = 2,31806333496276
 Log10 (209) = 2,32014628611105
 Log10 (210) = 2,32221929473392
 Log10 (211) = 2,32428245529769
 Log10 (212) = 2,32633586092875
 Log10 (213) = 2,32837960343874
 Log10 (214) = 2,33041377334919
 Log10 (215) = 2,33243845991561
 Log10 (216) = 2,33445375115093
 Log10 (217) = 2,33645973384853
 Log10 (218) = 2,3384564936046
 Log10 (219) = 2,34044411484012
 Log10 (220) = 2,34242268082221
 Log10 (221) = 2,34439227368511
 Log10 (222) = 2,34635297445064
 Log10 (223) = 2,34830486304816
 Log10 (224) = 2,35024801833416
 Log10 (225) = 2,35218251811136
 Log10 (226) = 2,3541084391474
 Log10 (227) = 2,35602585719312
 Log10 (228) = 2,35793484700045
 Log10 (229) = 2,35983548233989
 Log10 (230) = 2,36172783601759
 Log10 (231) = 2,36361197989214
 Log10 (232) = 2,3654879848909
 Log10 (233) = 2,36735592102602
 Log10 (234) = 2,36921585741014
 Log10 (235) = 2,37106786227174
 Log10 (236) = 2,37291200297011
 Log10 (237) = 2,3747483460101
 Log10 (238) = 2,37657695705651
 Log10 (239) = 2,37839790094814
 Log10 (240) = 2,38021124171161
 Log10 (241) = 2,38201704257487
 Log10 (242) = 2,38381536598043
 Log10 (243) = 2,38560627359831
 Log10 (244) = 2,38738982633873
 Log10 (245) = 2,38916608436453
 Log10 (246) = 2,39093510710338
 Log10 (247) = 2,39269695325967
 Log10 (248) = 2,39445168082622
 Log10 (249) = 2,39619934709574
 Log10 (250) = 2,39794000867204
 Log10 (251) = 2,39967372148104
 Log10 (252) = 2,40140054078154
 Log10 (253) = 2,40312052117582
 Log10 (254) = 2,40483371661994
 Log10 (255) = 2,40654018043396
 Log10 (256) = 2,40823996531185
 Log10 (257) = 2,40993312333129
 Log10 (258) = 2,41161970596323
 Log10 (259) = 2,41329976408125
 Log10 (260) = 2,41497334797082
 Log10 (261) = 2,41664050733828
 Log10 (262) = 2,41830129131975
 Log10 (263) = 2,41995574848976
 Log10 (264) = 2,42160392686983
 Log10 (265) = 2,42324587393681
 Log10 (266) = 2,42488163663107
 Log10 (267) = 2,42651126136458
 Log10 (268) = 2,42813479402879
 Log10 (269) = 2,42975228000241
 Log10 (270) = 2,43136376415899
 Log10 (271) = 2,43296929087441
 Log10 (272) = 2,4345689040342
 Log10 (273) = 2,43616264704076
 Log10 (274) = 2,43775056282039
 Log10 (275) = 2,43933269383026
 Log10 (276) = 2,44090908206522
 Log10 (277) = 2,44247976906445
 Log10 (278) = 2,44404479591808
 Log10 (279) = 2,4456042032736
 Log10 (280) = 2,44715803134222
 Log10 (281) = 2,44870631990508
 Log10 (282) = 2,45024910831936
 Log10 (283) = 2,45178643552429
 Log10 (284) = 2,45331834004704
 Log10 (285) = 2,45484486000851
 Log10 (286) = 2,45636603312904
 Log10 (287) = 2,45788189673399
 Log10 (288) = 2,45939248775923
 Log10 (289) = 2,46089784275655
 Log10 (290) = 2,46239799789896
 Log10 (291) = 2,46389298898591
 Log10 (292) = 2,46538285144842
 Log10 (293) = 2,46686762035411
 Log10 (294) = 2,46834733041216
 Log10 (295) = 2,46982201597816
 Log10 (296) = 2,47129171105894
 Log10 (297) = 2,47275644931721
 Log10 (298) = 2,47421626407626
 Log10 (299) = 2,47567118832443
 Log10 (300) = 2,47712125471966
 Log10 (301) = 2,47856649559384
 Log10 (302) = 2,48000694295715
 Log10 (303) = 2,4814426285023
 Log10 (304) = 2,48287358360875
 Log10 (305) = 2,48429983934679
 Log10 (306) = 2,48572142648158
 Log10 (307) = 2,48713837547719
 Log10 (308) = 2,48855071650044
 Log10 (309) = 2,48995847942483
 Log10 (310) = 2,49136169383427
 Log10 (311) = 2,49276038902684
 Log10 (312) = 2,49415459401844
 Log10 (313) = 2,49554433754645
 Log10 (314) = 2,49692964807321
 Log10 (315) = 2,4983105537896
 Log10 (316) = 2,4996870826184
 Log10 (317) = 2,50105926221775
 Log10 (318) = 2,50242711998443
 Log10 (319) = 2,50379068305718
 Log10 (320) = 2,50514997831991
 Log10 (321) = 2,50650503240487
 Log10 (322) = 2,50785587169583
 Log10 (323) = 2,5092025223311
 Log10 (324) = 2,51054501020661
 Log10 (325) = 2,51188336097887
 Log10 (326) = 2,51321760006794
 Log10 (327) = 2,51454775266029
 Log10 (328) = 2,51587384371168
 Log10 (329) = 2,51719589794997
 Log10 (330) = 2,51851393987789
 Log10 (331) = 2,51982799377572
 Log10 (332) = 2,52113808370404
 Log10 (333) = 2,52244423350632
 Log10 (334) = 2,52374646681156
 Log10 (335) = 2,52504480703685
 Log10 (336) = 2,52633927738984
 Log10 (337) = 2,52762990087134
 Log10 (338) = 2,52891670027765
 Log10 (339) = 2,53019969820308
 Log10 (340) = 2,53147891704225
 Log10 (341) = 2,5327543789925
 Log10 (342) = 2,53402610605613
 Log10 (343) = 2,53529412004277
 Log10 (344) = 2,53655844257153
 Log10 (345) = 2,53781909507327
 Log10 (346) = 2,53907609879278
 Log10 (347) = 2,54032947479087
 Log10 (348) = 2,54157924394658
 Log10 (349) = 2,54282542695918
 Log10 (350) = 2,54406804435028
 Log10 (351) = 2,54530711646582
 Log10 (352) = 2,54654266347813
 Log10 (353) = 2,54777470538782
 Log10 (354) = 2,54900326202579
 Log10 (355) = 2,55022835305509
 Log10 (356) = 2,55144999797288
 Log10 (357) = 2,55266821611219
 Log10 (358) = 2,55388302664387
 Log10 (359) = 2,55509444857832
 Log10 (360) = 2,55630250076729
 Log10 (361) = 2,55750720190566
 Log10 (362) = 2,55870857053317
 Log10 (363) = 2,55990662503611
 Log10 (364) = 2,56110138364906
 Log10 (365) = 2,56229286445647
 Log10 (366) = 2,56348108539441
 Log10 (367) = 2,56466606425209
 Log10 (368) = 2,56584781867352
 Log10 (369) = 2,56702636615906
 Log10 (370) = 2,56820172406699
 Log10 (371) = 2,56937390961505
 Log10 (372) = 2,5705429398819
 Log10 (373) = 2,57170883180869
 Log10 (374) = 2,57287160220048
 Log10 (375) = 2,57403126772772
 Log10 (376) = 2,57518784492766
 Log10 (377) = 2,57634135020579
 Log10 (378) = 2,57749179983723
 Log10 (379) = 2,57863920996807
 Log10 (380) = 2,57978359661681
 Log10 (381) = 2,58092497567562
 Log10 (382) = 2,58206336291171
 Log10 (383) = 2,58319877396862
 Log10 (384) = 2,58433122436753
 Log10 (385) = 2,5854607295085
 Log10 (386) = 2,58658730467176
 Log10 (387) = 2,58771096501891
 Log10 (388) = 2,58883172559421
 Log10 (389) = 2,58994960132571
 Log10 (390) = 2,5910646070265
 Log10 (391) = 2,59217675739587
 Log10 (392) = 2,59328606702046
 Log10 (393) = 2,59439255037543
 Log10 (394) = 2,59549622182557
 Log10 (395) = 2,59659709562646
 Log10 (396) = 2,59769518592551
 Log10 (397) = 2,59879050676312
 Log10 (398) = 2,59988307207369
 Log10 (399) = 2,60097289568675
 Log10 (400) = 2,60205999132796
 Log10 (401) = 2,60314437262018
 Log10 (402) = 2,60422605308447
 Log10 (403) = 2,60530504614111
 Log10 (404) = 2,60638136511061
 Log10 (405) = 2,60745502321467
 Log10 (406) = 2,60852603357719
 Log10 (407) = 2,60959440922522
 Log10 (408) = 2,61066016308988
 Log10 (409) = 2,61172330800734
 Log10 (410) = 2,61278385671974
 Log10 (411) = 2,61384182187607
 Log10 (412) = 2,61489721603313
 Log10 (413) = 2,6159500516564
 Log10 (414) = 2,6170003411209
 Log10 (415) = 2,61804809671209
 Log10 (416) = 2,61909333062674
 Log10 (417) = 2,62013605497376
 Log10 (418) = 2,62117628177504
 Log10 (419) = 2,6222140229663
 Log10 (420) = 2,6232492903979
 Log10 (421) = 2,62428209583567
 Log10 (422) = 2,62531245096167
 Log10 (423) = 2,62634036737504
 Log10 (424) = 2,62736585659273
 Log10 (425) = 2,62838893005031
 Log10 (426) = 2,62940959910272
 Log10 (427) = 2,63042787502502
 Log10 (428) = 2,63144376901317
 Log10 (429) = 2,63245729218472
 Log10 (430) = 2,63346845557959
 Log10 (431) = 2,63447727016073
 Log10 (432) = 2,63548374681491
 Log10 (433) = 2,63648789635337
 Log10 (434) = 2,63748972951251
 Log10 (435) = 2,63848925695464
 Log10 (436) = 2,63948648926859
 Log10 (437) = 2,64048143697042
 Log10 (438) = 2,6414741105041
 Log10 (439) = 2,64246452024212
 Log10 (440) = 2,64345267648619
 Log10 (441) = 2,64443858946784
 Log10 (442) = 2,64542226934909
 Log10 (443) = 2,64640372622307
 Log10 (444) = 2,64738297011462
 Log10 (445) = 2,64836001098093
 Log10 (446) = 2,64933485871214
 Log10 (447) = 2,65030752313194
 Log10 (448) = 2,65127801399814
 Log10 (449) = 2,65224634100332
 Log10 (450) = 2,65321251377534
 Log10 (451) = 2,65417654187796
 Log10 (452) = 2,65513843481138
 Log10 (453) = 2,65609820201283
 Log10 (454) = 2,6570558528571
 Log10 (455) = 2,65801139665711
 Log10 (456) = 2,65896484266443
 Log10 (457) = 2,65991620006985
 Log10 (458) = 2,66086547800387
 Log10 (459) = 2,66181268553726
 Log10 (460) = 2,66275783168157
 Log10 (461) = 2,66370092538965
 Log10 (462) = 2,66464197555613
 Log10 (463) = 2,66558099101795
 Log10 (464) = 2,66651798055488
 Log10 (465) = 2,66745295288995
 Log10 (466) = 2,66838591669
 Log10 (467) = 2,66931688056611
 Log10 (468) = 2,67024585307412
 Log10 (469) = 2,67117284271508
 Log10 (470) = 2,67209785793572
 Log10 (471) = 2,6730209071289
 Log10 (472) = 2,67394199863409
 Log10 (473) = 2,67486114073781
 Log10 (474) = 2,67577834167409
 Log10 (475) = 2,67669360962487
 Log10 (476) = 2,67760695272049
 Log10 (477) = 2,67851837904011
 Log10 (478) = 2,67942789661212
 Log10 (479) = 2,68033551341456
 Log10 (480) = 2,68124123737559
 Log10 (481) = 2,68214507637383
 Log10 (482) = 2,68304703823885
 Log10 (483) = 2,68394713075151
 Log10 (484) = 2,68484536164441
 Log10 (485) = 2,68574173860226
 Log10 (486) = 2,68663626926229
 Log10 (487) = 2,68752896121463
 Log10 (488) = 2,68841982200271
 Log10 (489) = 2,68930885912362
 Log10 (490) = 2,69019608002851
 Log10 (491) = 2,69108149212297
 Log10 (492) = 2,69196510276736
 Log10 (493) = 2,69284691927723
 Log10 (494) = 2,69372694892365
 Log10 (495) = 2,69460519893357
 Log10 (496) = 2,6954816764902
 Log10 (497) = 2,69635638873333
 Log10 (498) = 2,69722934275972
 Log10 (499) = 2,69810054562339
 Log10 (500) = 2,69897000433602Log10 (1) = 0
 Log10 (2) = 0,301029995663981
 Log10 (3) = 0,477121254719662
 Log10 (4) = 0,602059991327962
 Log10 (5) = 0,698970004336019
 Log10 (6) = 0,778151250383644
 Log10 (7) = 0,845098040014257
 Log10 (8) = 0,903089986991944
 Log10 (9) = 0,954242509439325
 Log10 (10) = 1
 Log10 (11) = 1,04139268515823
 Log10 (12) = 1,07918124604762
 Log10 (13) = 1,11394335230684
 Log10 (14) = 1,14612803567824
 Log10 (15) = 1,17609125905568
 Log10 (16) = 1,20411998265592
 Log10 (17) = 1,23044892137827
 Log10 (18) = 1,25527250510331
 Log10 (19) = 1,27875360095283
 Log10 (20) = 1,30102999566398
 Log10 (21) = 1,32221929473392
 Log10 (22) = 1,34242268082221
 Log10 (23) = 1,36172783601759
 Log10 (24) = 1,38021124171161
 Log10 (25) = 1,39794000867204
 Log10 (26) = 1,41497334797082
 Log10 (27) = 1,43136376415899
 Log10 (28) = 1,44715803134222
 Log10 (29) = 1,46239799789896
 Log10 (30) = 1,47712125471966
 Log10 (31) = 1,49136169383427
 Log10 (32) = 1,50514997831991
 Log10 (33) = 1,51851393987789
 Log10 (34) = 1,53147891704226
 Log10 (35) = 1,54406804435028
 Log10 (36) = 1,55630250076729
 Log10 (37) = 1,56820172406699
 Log10 (38) = 1,57978359661681
 Log10 (39) = 1,5910646070265
 Log10 (40) = 1,60205999132796
 Log10 (41) = 1,61278385671974
 Log10 (42) = 1,6232492903979
 Log10 (43) = 1,63346845557959
 Log10 (44) = 1,64345267648619
 Log10 (45) = 1,65321251377534
 Log10 (46) = 1,66275783168157
 Log10 (47) = 1,67209785793572
 Log10 (48) = 1,68124123737559
 Log10 (49) = 1,69019608002851
 Log10 (50) = 1,69897000433602
 Log10 (51) = 1,70757017609794
 Log10 (52) = 1,7160033436348
 Log10 (53) = 1,72427586960079
 Log10 (54) = 1,73239375982297
 Log10 (55) = 1,74036268949424
 Log10 (56) = 1,7481880270062
 Log10 (57) = 1,75587485567249
 Log10 (58) = 1,76342799356294
 Log10 (59) = 1,77085201164214
 Log10 (60) = 1,77815125038364
 Log10 (61) = 1,78532983501077
 Log10 (62) = 1,79239168949825
 Log10 (63) = 1,79934054945358
 Log10 (64) = 1,80617997398389
 Log10 (65) = 1,81291335664286
 Log10 (66) = 1,81954393554187
 Log10 (67) = 1,82607480270083
 Log10 (68) = 1,83250891270624
 Log10 (69) = 1,83884909073726
 Log10 (70) = 1,84509804001426
 Log10 (71) = 1,85125834871908
 Log10 (72) = 1,85733249643127
 Log10 (73) = 1,86332286012046
 Log10 (74) = 1,86923171973098
 Log10 (75) = 1,8750612633917
 Log10 (76) = 1,88081359228079
 Log10 (77) = 1,88649072517248
 Log10 (78) = 1,89209460269048
 Log10 (79) = 1,89762709129044
 Log10 (80) = 1,90308998699194
 Log10 (81) = 1,90848501887865
 Log10 (82) = 1,91381385238372
 Log10 (83) = 1,91907809237607
 Log10 (84) = 1,92427928606188
 Log10 (85) = 1,92941892571429
 Log10 (86) = 1,93449845124357
 Log10 (87) = 1,93951925261862
 Log10 (88) = 1,94448267215017
 Log10 (89) = 1,94939000664491
 Log10 (90) = 1,95424250943932
 Log10 (91) = 1,95904139232109
 Log10 (92) = 1,96378782734556
 Log10 (93) = 1,96848294855394
 Log10 (94) = 1,9731278535997
 Log10 (95) = 1,97772360528885
 Log10 (96) = 1,98227123303957
 Log10 (97) = 1,98677173426624
 Log10 (98) = 1,99122607569249
 Log10 (99) = 1,99563519459755
 Log10 (100) = 2
 Log10 (101) = 2,00432137378264
 Log10 (102) = 2,00860017176192
 Log10 (103) = 2,01283722470517
 Log10 (104) = 2,01703333929878
 Log10 (105) = 2,02118929906994
 Log10 (106) = 2,02530586526477
 Log10 (107) = 2,02938377768521
 Log10 (108) = 2,03342375548695
 Log10 (109) = 2,03742649794062
 Log10 (110) = 2,04139268515822
 Log10 (111) = 2,04532297878666
 Log10 (112) = 2,04921802267018
 Log10 (113) = 2,05307844348342
 Log10 (114) = 2,05690485133647
 Log10 (115) = 2,06069784035361
 Log10 (116) = 2,06445798922692
 Log10 (117) = 2,06818586174616
 Log10 (118) = 2,07188200730613
 Log10 (119) = 2,07554696139253
 Log10 (120) = 2,07918124604762
 Log10 (121) = 2,08278537031645
 Log10 (122) = 2,08635983067475
 Log10 (123) = 2,0899051114394
 Log10 (124) = 2,09342168516224
 Log10 (125) = 2,09691001300806
 Log10 (126) = 2,10037054511756
 Log10 (127) = 2,10380372095596
 Log10 (128) = 2,10720996964787
 Log10 (129) = 2,11058971029925
 Log10 (130) = 2,11394335230684
 Log10 (131) = 2,11727129565576
 Log10 (132) = 2,12057393120585
 Log10 (133) = 2,12385164096709
 Log10 (134) = 2,12710479836481
 Log10 (135) = 2,13033376849501
 Log10 (136) = 2,13353890837022
 Log10 (137) = 2,13672056715641
 Log10 (138) = 2,13987908640124
 Log10 (139) = 2,14301480025409
 Log10 (140) = 2,14612803567824
 Log10 (141) = 2,14921911265538
 Log10 (142) = 2,15228834438306
 Log10 (143) = 2,15533603746506
 Log10 (144) = 2,15836249209525
 Log10 (145) = 2,16136800223497
 Log10 (146) = 2,16435285578444
 Log10 (147) = 2,16731733474818
 Log10 (148) = 2,17026171539496
 Log10 (149) = 2,17318626841227
 Log10 (150) = 2,17609125905568
 Log10 (151) = 2,17897694729317
 Log10 (152) = 2,18184358794477
 Log10 (153) = 2,1846914308176
 Log10 (154) = 2,18752072083646
 Log10 (155) = 2,19033169817029
 Log10 (156) = 2,19312459835446
 Log10 (157) = 2,19589965240923
 Log10 (158) = 2,19865708695442
 Log10 (159) = 2,20139712432045
 Log10 (160) = 2,20411998265592
 Log10 (161) = 2,20682587603185
 Log10 (162) = 2,20951501454263
 Log10 (163) = 2,21218760440396
 Log10 (164) = 2,2148438480477
 Log10 (165) = 2,21748394421391
 Log10 (166) = 2,22010808804005
 Log10 (167) = 2,22271647114758
 Log10 (168) = 2,22530928172586
 Log10 (169) = 2,22788670461367
 Log10 (170) = 2,23044892137827
 Log10 (171) = 2,23299611039215
 Log10 (172) = 2,23552844690755
 Log10 (173) = 2,2380461031288
 Log10 (174) = 2,2405492482826
 Log10 (175) = 2,24303804868629
 Log10 (176) = 2,24551266781415
 Log10 (177) = 2,24797326636181
 Log10 (178) = 2,25042000230889
 Log10 (179) = 2,25285303097989
 Log10 (180) = 2,25527250510331
 Log10 (181) = 2,25767857486918
 Log10 (182) = 2,26007138798507
 Log10 (183) = 2,26245108973043
 Log10 (184) = 2,26481782300954
 Log10 (185) = 2,26717172840301
 Log10 (186) = 2,26951294421792
 Log10 (187) = 2,2718416065365
 Log10 (188) = 2,27415784926368
 Log10 (189) = 2,27646180417324
 Log10 (190) = 2,27875360095283
 Log10 (191) = 2,28103336724773
 Log10 (192) = 2,28330122870355
 Log10 (193) = 2,28555730900777
 Log10 (194) = 2,28780172993023
 Log10 (195) = 2,29003461136252
 Log10 (196) = 2,29225607135648
 Log10 (197) = 2,29446622616159
 Log10 (198) = 2,29666519026153
 Log10 (199) = 2,29885307640971
 Log10 (200) = 2,30102999566398
 Log10 (201) = 2,30319605742049
 Log10 (202) = 2,30535136944662
 Log10 (203) = 2,30749603791321
 Log10 (204) = 2,3096301674259
 Log10 (205) = 2,31175386105575
 Log10 (206) = 2,31386722036915
 Log10 (207) = 2,31597034545692
 Log10 (208) = 2,31806333496276
 Log10 (209) = 2,32014628611105
 Log10 (210) = 2,32221929473392
 Log10 (211) = 2,32428245529769
 Log10 (212) = 2,32633586092875
 Log10 (213) = 2,32837960343874
 Log10 (214) = 2,33041377334919
 Log10 (215) = 2,33243845991561
 Log10 (216) = 2,33445375115093
 Log10 (217) = 2,33645973384853
 Log10 (218) = 2,3384564936046
 Log10 (219) = 2,34044411484012
 Log10 (220) = 2,34242268082221
 Log10 (221) = 2,34439227368511
 Log10 (222) = 2,34635297445064
 Log10 (223) = 2,34830486304816
 Log10 (224) = 2,35024801833416
 Log10 (225) = 2,35218251811136
 Log10 (226) = 2,3541084391474
 Log10 (227) = 2,35602585719312
 Log10 (228) = 2,35793484700045
 Log10 (229) = 2,35983548233989
 Log10 (230) = 2,36172783601759
 Log10 (231) = 2,36361197989214
 Log10 (232) = 2,3654879848909
 Log10 (233) = 2,36735592102602
 Log10 (234) = 2,36921585741014
 Log10 (235) = 2,37106786227174
 Log10 (236) = 2,37291200297011
 Log10 (237) = 2,3747483460101
 Log10 (238) = 2,37657695705651
 Log10 (239) = 2,37839790094814
 Log10 (240) = 2,38021124171161
 Log10 (241) = 2,38201704257487
 Log10 (242) = 2,38381536598043
 Log10 (243) = 2,38560627359831
 Log10 (244) = 2,38738982633873
 Log10 (245) = 2,38916608436453
 Log10 (246) = 2,39093510710338
 Log10 (247) = 2,39269695325967
 Log10 (248) = 2,39445168082622
 Log10 (249) = 2,39619934709574
 Log10 (250) = 2,39794000867204
 Log10 (251) = 2,39967372148104
 Log10 (252) = 2,40140054078154
 Log10 (253) = 2,40312052117582
 Log10 (254) = 2,40483371661994
 Log10 (255) = 2,40654018043396
 Log10 (256) = 2,40823996531185
 Log10 (257) = 2,40993312333129
 Log10 (258) = 2,41161970596323
 Log10 (259) = 2,41329976408125
 Log10 (260) = 2,41497334797082
 Log10 (261) = 2,41664050733828
 Log10 (262) = 2,41830129131975
 Log10 (263) = 2,41995574848976
 Log10 (264) = 2,42160392686983
 Log10 (265) = 2,42324587393681
 Log10 (266) = 2,42488163663107
 Log10 (267) = 2,42651126136458
 Log10 (268) = 2,42813479402879
 Log10 (269) = 2,42975228000241
 Log10 (270) = 2,43136376415899
 Log10 (271) = 2,43296929087441
 Log10 (272) = 2,4345689040342
 Log10 (273) = 2,43616264704076
 Log10 (274) = 2,43775056282039
 Log10 (275) = 2,43933269383026
 Log10 (276) = 2,44090908206522
 Log10 (277) = 2,44247976906445
 Log10 (278) = 2,44404479591808
 Log10 (279) = 2,4456042032736
 Log10 (280) = 2,44715803134222
 Log10 (281) = 2,44870631990508
 Log10 (282) = 2,45024910831936
 Log10 (283) = 2,45178643552429
 Log10 (284) = 2,45331834004704
 Log10 (285) = 2,45484486000851
 Log10 (286) = 2,45636603312904
 Log10 (287) = 2,45788189673399
 Log10 (288) = 2,45939248775923
 Log10 (289) = 2,46089784275655
 Log10 (290) = 2,46239799789896
 Log10 (291) = 2,46389298898591
 Log10 (292) = 2,46538285144842
 Log10 (293) = 2,46686762035411
 Log10 (294) = 2,46834733041216
 Log10 (295) = 2,46982201597816
 Log10 (296) = 2,47129171105894
 Log10 (297) = 2,47275644931721
 Log10 (298) = 2,47421626407626
 Log10 (299) = 2,47567118832443
 Log10 (300) = 2,47712125471966
 Log10 (301) = 2,47856649559384
 Log10 (302) = 2,48000694295715
 Log10 (303) = 2,4814426285023
 Log10 (304) = 2,48287358360875
 Log10 (305) = 2,48429983934679
 Log10 (306) = 2,48572142648158
 Log10 (307) = 2,48713837547719
 Log10 (308) = 2,48855071650044
 Log10 (309) = 2,48995847942483
 Log10 (310) = 2,49136169383427
 Log10 (311) = 2,49276038902684
 Log10 (312) = 2,49415459401844
 Log10 (313) = 2,49554433754645
 Log10 (314) = 2,49692964807321
 Log10 (315) = 2,4983105537896
 Log10 (316) = 2,4996870826184
 Log10 (317) = 2,50105926221775
 Log10 (318) = 2,50242711998443
 Log10 (319) = 2,50379068305718
 Log10 (320) = 2,50514997831991
 Log10 (321) = 2,50650503240487
 Log10 (322) = 2,50785587169583
 Log10 (323) = 2,5092025223311
 Log10 (324) = 2,51054501020661
 Log10 (325) = 2,51188336097887
 Log10 (326) = 2,51321760006794
 Log10 (327) = 2,51454775266029
 Log10 (328) = 2,51587384371168
 Log10 (329) = 2,51719589794997
 Log10 (330) = 2,51851393987789
 Log10 (331) = 2,51982799377572
 Log10 (332) = 2,52113808370404
 Log10 (333) = 2,52244423350632
 Log10 (334) = 2,52374646681156
 Log10 (335) = 2,52504480703685
 Log10 (336) = 2,52633927738984
 Log10 (337) = 2,52762990087134
 Log10 (338) = 2,52891670027765
 Log10 (339) = 2,53019969820308
 Log10 (340) = 2,53147891704225
 Log10 (341) = 2,5327543789925
 Log10 (342) = 2,53402610605613
 Log10 (343) = 2,53529412004277
 Log10 (344) = 2,53655844257153
 Log10 (345) = 2,53781909507327
 Log10 (346) = 2,53907609879278
 Log10 (347) = 2,54032947479087
 Log10 (348) = 2,54157924394658
 Log10 (349) = 2,54282542695918
 Log10 (350) = 2,54406804435028
 Log10 (351) = 2,54530711646582
 Log10 (352) = 2,54654266347813
 Log10 (353) = 2,54777470538782
 Log10 (354) = 2,54900326202579
 Log10 (355) = 2,55022835305509
 Log10 (356) = 2,55144999797288
 Log10 (357) = 2,55266821611219
 Log10 (358) = 2,55388302664387
 Log10 (359) = 2,55509444857832
 Log10 (360) = 2,55630250076729
 Log10 (361) = 2,55750720190566
 Log10 (362) = 2,55870857053317
 Log10 (363) = 2,55990662503611
 Log10 (364) = 2,56110138364906
 Log10 (365) = 2,56229286445647
 Log10 (366) = 2,56348108539441
 Log10 (367) = 2,56466606425209
 Log10 (368) = 2,56584781867352
 Log10 (369) = 2,56702636615906
 Log10 (370) = 2,56820172406699
 Log10 (371) = 2,56937390961505
 Log10 (372) = 2,5705429398819
 Log10 (373) = 2,57170883180869
 Log10 (374) = 2,57287160220048
 Log10 (375) = 2,57403126772772
 Log10 (376) = 2,57518784492766
 Log10 (377) = 2,57634135020579
 Log10 (378) = 2,57749179983723
 Log10 (379) = 2,57863920996807
 Log10 (380) = 2,57978359661681
 Log10 (381) = 2,58092497567562
 Log10 (382) = 2,58206336291171
 Log10 (383) = 2,58319877396862
 Log10 (384) = 2,58433122436753
 Log10 (385) = 2,5854607295085
 Log10 (386) = 2,58658730467176
 Log10 (387) = 2,58771096501891
 Log10 (388) = 2,58883172559421
 Log10 (389) = 2,58994960132571
 Log10 (390) = 2,5910646070265
 Log10 (391) = 2,59217675739587
 Log10 (392) = 2,59328606702046
 Log10 (393) = 2,59439255037543
 Log10 (394) = 2,59549622182557
 Log10 (395) = 2,59659709562646
 Log10 (396) = 2,59769518592551
 Log10 (397) = 2,59879050676312
 Log10 (398) = 2,59988307207369
 Log10 (399) = 2,60097289568675
 Log10 (400) = 2,60205999132796
 Log10 (401) = 2,60314437262018
 Log10 (402) = 2,60422605308447
 Log10 (403) = 2,60530504614111
 Log10 (404) = 2,60638136511061
 Log10 (405) = 2,60745502321467
 Log10 (406) = 2,60852603357719
 Log10 (407) = 2,60959440922522
 Log10 (408) = 2,61066016308988
 Log10 (409) = 2,61172330800734
 Log10 (410) = 2,61278385671974
 Log10 (411) = 2,61384182187607
 Log10 (412) = 2,61489721603313
 Log10 (413) = 2,6159500516564
 Log10 (414) = 2,6170003411209
 Log10 (415) = 2,61804809671209
 Log10 (416) = 2,61909333062674
 Log10 (417) = 2,62013605497376
 Log10 (418) = 2,62117628177504
 Log10 (419) = 2,6222140229663
 Log10 (420) = 2,6232492903979
 Log10 (421) = 2,62428209583567
 Log10 (422) = 2,62531245096167
 Log10 (423) = 2,62634036737504
 Log10 (424) = 2,62736585659273
 Log10 (425) = 2,62838893005031
 Log10 (426) = 2,62940959910272
 Log10 (427) = 2,63042787502502
 Log10 (428) = 2,63144376901317
 Log10 (429) = 2,63245729218472
 Log10 (430) = 2,63346845557959
 Log10 (431) = 2,63447727016073
 Log10 (432) = 2,63548374681491
 Log10 (433) = 2,63648789635337
 Log10 (434) = 2,63748972951251
 Log10 (435) = 2,63848925695464
 Log10 (436) = 2,63948648926859
 Log10 (437) = 2,64048143697042
 Log10 (438) = 2,6414741105041
 Log10 (439) = 2,64246452024212
 Log10 (440) = 2,64345267648619
 Log10 (441) = 2,64443858946784
 Log10 (442) = 2,64542226934909
 Log10 (443) = 2,64640372622307
 Log10 (444) = 2,64738297011462
 Log10 (445) = 2,64836001098093
 Log10 (446) = 2,64933485871214
 Log10 (447) = 2,65030752313194
 Log10 (448) = 2,65127801399814
 Log10 (449) = 2,65224634100332
 Log10 (450) = 2,65321251377534
 Log10 (451) = 2,65417654187796
 Log10 (452) = 2,65513843481138
 Log10 (453) = 2,65609820201283
 Log10 (454) = 2,6570558528571
 Log10 (455) = 2,65801139665711
 Log10 (456) = 2,65896484266443
 Log10 (457) = 2,65991620006985
 Log10 (458) = 2,66086547800387
 Log10 (459) = 2,66181268553726
 Log10 (460) = 2,66275783168157
 Log10 (461) = 2,66370092538965
 Log10 (462) = 2,66464197555613
 Log10 (463) = 2,66558099101795
 Log10 (464) = 2,66651798055488
 Log10 (465) = 2,66745295288995
 Log10 (466) = 2,66838591669
 Log10 (467) = 2,66931688056611
 Log10 (468) = 2,67024585307412
 Log10 (469) = 2,67117284271508
 Log10 (470) = 2,67209785793572
 Log10 (471) = 2,6730209071289
 Log10 (472) = 2,67394199863409
 Log10 (473) = 2,67486114073781
 Log10 (474) = 2,67577834167409
 Log10 (475) = 2,67669360962487
 Log10 (476) = 2,67760695272049
 Log10 (477) = 2,67851837904011
 Log10 (478) = 2,67942789661212
 Log10 (479) = 2,68033551341456
 Log10 (480) = 2,68124123737559
 Log10 (481) = 2,68214507637383
 Log10 (482) = 2,68304703823885
 Log10 (483) = 2,68394713075151
 Log10 (484) = 2,68484536164441
 Log10 (485) = 2,68574173860226
 Log10 (486) = 2,68663626926229
 Log10 (487) = 2,68752896121463
 Log10 (488) = 2,68841982200271
 Log10 (489) = 2,68930885912362
 Log10 (490) = 2,69019608002851
 Log10 (491) = 2,69108149212297
 Log10 (492) = 2,69196510276736
 Log10 (493) = 2,69284691927723
 Log10 (494) = 2,69372694892365
 Log10 (495) = 2,69460519893357
 Log10 (496) = 2,6954816764902
 Log10 (497) = 2,69635638873333
 Log10 (498) = 2,69722934275972
 Log10 (499) = 2,69810054562339
 Log10 (500) = 2,69897000433602

História do logaritimo

Os logaritmos, como instrumento de cálculo, surgiram para realizar simplificações, uma vez que transformam multiplicações e divisões nas operações mais básicas como soma e subtração.
O mérito da invenção foi dado ao escocês John Napier, embora não tivesse descoberto tudo sozinho.
Napier era um Barão e gostava de Matemática, mas não era matemático profissional. Seu trabalho deu o impulso final para o emprego universal da notação decimal, com o uso sistemático de casas decimais depois da vírgula para representar frações decimais.
Uma das necessidades que levaram ao pensamento de descobrir meios matemáticos para solucionar problemas foram as grandes navegações, a astronomia e operações a serem efetuadas contendo muitos dígitos, o que as tornava mais difíceis, principalmente no caso de multiplicações e divisões.
Na invenção do logaritmo, Napier trabalhou durante vinte anos antes de publicar seus resultados, isso ocorreu em 1614, quando publicou “mirifici logarithmorum canonis descriptio” (uma descrição da maravilha dos logaritmos).
A publicação em 1614 do sistema de logaritmos teve sucesso imediato, e entre seus admiradores mais entusiásticos estava Henry Briggs, professor de Geometria em Oxford. Em 1615 ele visitou Napier em sua casa na Escócia, e lá eles discutiram possíveis modificações no método dos logaritmos. Briggs propôs o uso de potências de dez, e Napier que já havia pensado nessa possibilidade e concordava. Napier uma vez tinha proposto uma tabela .
Os dois finalmente concordaram em que o logaritmo de 1 deveria ser 0 e o logaritmo de 10 deveria ser 1. Mas Napier já não tinha energia suficiente para por em prática essas ideias, pois morrera em 1617. Por isso recaiu sobre Briggs a tarefa de construir a primeira tabela de logaritmos comuns.
Ficou sugerido até agora que a invenção dos logaritmos foi obra de um só homem, mas tal impressão não deve permanecer. Napier de fato foi o primeiro a publicar uma obra sobre logaritmos, mas idéias muito semelhantes foram desenvolvidas independentemente na Suíça por Jobst Bürgui mais ou menos ao mesmo tempo. Na verdade, é possível que a idéia de logaritmo tenha ocorrido a Bürgui em 1588, o que seria seis anos antes de Napier começar a trabalhar na mesma direção. Porém Bürgui só publicou seus resultados em 1620. As diferenças entre as obras dos dois homens estão principalmente na terminologia e nos valores numéricos, os princípios fundamentais eram os mesmos.

Video aula sobre logaritimos

DETERMINAÇÃO DO VALOR DE UM LOGARITMO

Além da base 10,há outras base muito empregada em problemas científicos,conhecida como base e , em que e representa um numero irracional cujo valor aproximado é 2,718 .

O logaritmo de um numero x na base e é indicado usualmente por ln x , em vez de logex , e é conhecido por logaratmo natural de x ou logaritmo neperiano de x , em homenagem a Jonh Napier.
para efetuar cálculos que envolvem logaritmos,podemos utilizar uma calculadora científica. observe o uso de algumas teclas:

* a tecla log serve para calcular o logaritmo na base 10. se o logaritmo estiver na base e , utilizamos a tecla (ln) .


* a tecla (10x), serve para calcular um logaritmando de base 10.

*digita-se o valor x do logaritmo e aperta-se (10x) . se o logaritmando se refere a um logaritmo neperiano , utilizamos a tecla (ex) 

EXEMPLO:

*para calcular log47 , digita-se 47 e aperta-se a tela (log) . assim , obtemos

log47=1,6720979

*para calcular o valor de b na expressão log b = 1,4624 e depois apertamos a tecla 10x . logo b=29. 

*calcular ln 9, digitamos 9 e apertamos a tecla ln . De forma que ln 9 = 2,197225


*para calcular o valor de b na expressão ln b = 2,0794 , teclamos 2,0794 e depois apertamos a tecla ex . logo , b =8 .