Tabela de valores dos logaritmos:
|
nº / base
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
|
2
|
1,0000
|
0,6309
|
0,5000
|
0,4307
|
0,3869
|
0,3562
|
0,3333
|
0,3155
|
|
3
|
1,5850
|
1,0000
|
0,7925
|
0,6826
|
0,6131
|
0,5646
|
0,5283
|
0,5000
|
|
4
|
2,0000
|
1,2619
|
1,0000
|
0,8614
|
0,7737
|
0,7124
|
0,6667
|
0,6309
|
|
5
|
2,3219
|
1,4650
|
1,1610
|
1,0000
|
0,8982
|
0,8271
|
0,7740
|
0,7325
|
|
6
|
2,5850
|
1,6309
|
1,2925
|
1,1133
|
1,0000
|
0,9208
|
0,8617
|
0,8155
|
|
7
|
2,8074
|
1,7712
|
1,4037
|
1,2091
|
1,0860
|
1,0000
|
0,9358
|
0,8856
|
|
8
|
3,0000
|
1,8928
|
1,5000
|
1,2920
|
1,1606
|
1,0686
|
1,0000
|
0,9464
|
|
9
|
3,1699
|
2,0000
|
1,5850
|
1,3652
|
1,2263
|
1,1292
|
1,0566
|
1,0000
|
|
10
|
3,3219
|
2,0959
|
1,6610
|
1,4307
|
1,2851
|
1,1833
|
1,1073
|
1,0480
|
|
11
|
3,4594
|
2,1827
|
1,7297
|
1,4899
|
1,3383
|
1,2323
|
1,1531
|
1,0913
|
|
12
|
3,5850
|
2,2619
|
1,7925
|
1,5440
|
1,3869
|
1,2770
|
1,1950
|
1,1309
|
|
13
|
3,7004
|
2,3347
|
1,8502
|
1,5937
|
1,4315
|
1,3181
|
1,2335
|
1,1674
|
|
14
|
3,8074
|
2,4022
|
1,9037
|
1,6397
|
1,4729
|
1,3562
|
1,2691
|
1,2011
|
|
15
|
3,9069
|
2,4650
|
1,9534
|
1,6826
|
1,5114
|
1,3917
|
1,3023
|
1,2325
|
|
16
|
4,0000
|
2,5237
|
2,0000
|
1,7227
|
1,5474
|
1,4248
|
1,3333
|
1,2619
|
|
17
|
4,0875
|
2,5789
|
2,0437
|
1,7604
|
1,5812
|
1,4560
|
1,3625
|
1,2895
|
|
18
|
4,1699
|
2,6309
|
2,0850
|
1,7959
|
1,6131
|
1,4854
|
1,3900
|
1,3155
|
|
19
|
4,2479
|
2,6801
|
2,1240
|
1,8295
|
1,6433
|
1,5131
|
1,4160
|
1,3401
|
|
20
|
4,3219
|
2,7268
|
2,1610
|
1,8614
|
1,6720
|
1,5395
|
1,4406
|
1,3634
|
|
21
|
4,3923
|
2,7712
|
2,1962
|
1,8917
|
1,6992
|
1,5646
|
1,4641
|
1,3856
|
|
22
|
4,4594
|
2,8136
|
2,2297
|
1,9206
|
1,7251
|
1,5885
|
1,4865
|
1,4068
|
|
23
|
4,5236
|
2,8540
|
2,2618
|
1,9482
|
1,7500
|
1,6113
|
1,5079
|
1,4270
|
|
24
|
4,5850
|
2,8928
|
2,2925
|
1,9746
|
1,7737
|
1,6332
|
1,5283
|
1,4464
|
|
25
|
4,6439
|
2,9299
|
2,3219
|
2,0000
|
1,7965
|
1,6542
|
1,5480
|
1,4650
|
|
26
|
4,7004
|
2,9656
|
2,3502
|
2,0244
|
1,8184
|
1,6743
|
1,5668
|
1,4828
|
|
27
|
4,7549
|
3,0000
|
2,3774
|
2,0478
|
1,8394
|
1,6937
|
1,5850
|
1,5000
|
|
28
|
4,8074
|
3,0331
|
2,4037
|
2,0704
|
1,8597
|
1,7124
|
1,6025
|
1,5166
|
|
29
|
4,8580
|
3,0650
|
2,4290
|
2,0922
|
1,8793
|
1,7304
|
1,6193
|
1,5325
|
|
30
|
4,9069
|
3,0959
|
2,4534
|
2,1133
|
1,8982
|
1,7479
|
1,6356
|
1,5480
|
|
31
|
4,9542
|
3,1257
|
2,4771
|
2,1337
|
1,9165
|
1,7647
|
1,6514
|
1,5629
|
|
32
|
5,0000
|
3,1546
|
2,5000
|
2,1534
|
1,9343
|
1,7810
|
1,6667
|
1,5773
|
|
33
|
5,0444
|
3,1827
|
2,5222
|
2,1725
|
1,9514
|
1,7968
|
1,6815
|
1,5913
|
|
34
|
5,0875
|
3,2098
|
2,5437
|
2,1911
|
1,9681
|
1,8122
|
1,6958
|
1,6049
|
|
35
|
5,1293
|
3,2362
|
2,5646
|
2,2091
|
1,9843
|
1,8271
|
1,7098
|
1,6181
|
|
36
|
5,1699
|
3,2619
|
2,5850
|
2,2266
|
2,0000
|
1,8416
|
1,7233
|
1,6309
|
|
37
|
5,2095
|
3,2868
|
2,6047
|
2,2436
|
2,0153
|
1,8556
|
1,7365
|
1,6434
|
|
38
|
5,2479
|
3,3111
|
2,6240
|
2,2602
|
2,0302
|
1,8693
|
1,7493
|
1,6555
|
|
39
|
5,2854
|
3,3347
|
2,6427
|
2,2763
|
2,0447
|
1,8827
|
1,7618
|
1,6674
|
|
40
|
5,3219
|
3,3578
|
2,6610
|
2,2920
|
2,0588
|
1,8957
|
1,7740
|
1,6789
|
|
41
|
5,3576
|
3,3802
|
2,6788
|
2,3074
|
2,0726
|
1,9084
|
1,7859
|
1,6901
|
|
42
|
5,3923
|
3,4022
|
2,6962
|
2,3223
|
2,0860
|
1,9208
|
1,7974
|
1,7011
|
|
43
|
5,4263
|
3,4236
|
2,7131
|
2,3370
|
2,0992
|
1,9329
|
1,8088
|
1,7118
|
|
44
|
5,4594
|
3,4445
|
2,7297
|
2,3512
|
2,1120
|
1,9447
|
1,8198
|
1,7223
|
|
45
|
5,4919
|
3,4650
|
2,7459
|
2,3652
|
2,1245
|
1,9562
|
1,8306
|
1,7325
|
|
46
|
5,5236
|
3,4850
|
2,7618
|
2,3789
|
2,1368
|
1,9675
|
1,8412
|
1,7425
|
|
47
|
5,5546
|
3,5046
|
2,7773
|
2,3922
|
2,1488
|
1,9786
|
1,8515
|
1,7523
|
|
48
|
5,5850
|
3,5237
|
2,7925
|
2,4053
|
2,1606
|
1,9894
|
1,8617
|
1,7619
|
|
49
|
5,6147
|
3,5425
|
2,8074
|
2,4181
|
2,1721
|
2,0000
|
1,8716
|
1,7712
|
|
50
|
5,6439
|
3,5609
|
2,8219
|
2,4307
|
2,1833
|
2,0104
|
1,8813
|
1,7804
|
|
51
|
5,6724
|
3,5789
|
2,8362
|
2,4430
|
2,1944
|
2,0206
|
1,8908
|
1,7895
|
|
52
|
5,7004
|
3,5966
|
2,8502
|
2,4550
|
2,2052
|
2,0305
|
1,9001
|
1,7983
|
|
53
|
5,7279
|
3,6139
|
2,8640
|
2,4669
|
2,2159
|
2,0403
|
1,9093
|
1,8070
|
|
54
|
5,7549
|
3,6309
|
2,8774
|
2,4785
|
2,2263
|
2,0499
|
1,9183
|
1,8155
|
|
55
|
5,7814
|
3,6476
|
2,8907
|
2,4899
|
2,2365
|
2,0594
|
1,9271
|
1,8238
|
|
56
|
5,8074
|
3,6640
|
2,9037
|
2,5011
|
2,2466
|
2,0686
|
1,9358
|
1,8320
|
|
57
|
5,8329
|
3,6801
|
2,9164
|
2,5121
|
2,2565
|
2,0777
|
1,9443
|
1,8401
|
|
58
|
5,8580
|
3,6960
|
2,9290
|
2,5229
|
2,2662
|
2,0867
|
1,9527
|
1,8480
|
|
59
|
5,8826
|
3,7115
|
2,9413
|
2,5335
|
2,2757
|
2,0954
|
1,9609
|
1,8558
|
|
60
|
5,9069
|
3,7268
|
2,9534
|
2,5440
|
2,2851
|
2,1041
|
1,9690
|
1,8634
|
|
61
|
5,9307
|
3,7419
|
2,9654
|
2,5542
|
2,2943
|
2,1126
|
1,9769
|
1,8709
|
|
62
|
5,9542
|
3,7567
|
2,9771
|
2,5643
|
2,3034
|
2,1209
|
1,9847
|
1,8783
|
|
63
|
5,9773
|
3,7712
|
2,9886
|
2,5743
|
2,3123
|
2,1292
|
1,9924
|
1,8856
|
|
64
|
6,0000
|
3,7856
|
3,0000
|
2,5841
|
2,3211
|
2,1372
|
2,0000
|
1,8928
|
|
65
|
6,0224
|
3,7997
|
3,0112
|
2,5937
|
2,3298
|
2,1452
|
2,0075
|
1,8998
|
|
66
|
6,0444
|
3,8136
|
3,0222
|
2,6032
|
2,3383
|
2,1531
|
2,0148
|
1,9068
|
|
67
|
6,0661
|
3,8273
|
3,0330
|
2,6125
|
2,3467
|
2,1608
|
2,0220
|
1,9136
|
|
68
|
6,0875
|
3,8408
|
3,0437
|
2,6217
|
2,3550
|
2,1684
|
2,0292
|
1,9204
|
|
69
|
6,1085
|
3,8540
|
3,0543
|
2,6308
|
2,3631
|
2,1759
|
2,0362
|
1,9270
|
|
70
|
6,1293
|
3,8671
|
3,0646
|
2,6397
|
2,3711
|
2,1833
|
2,0431
|
1,9336
|
|
71
|
6,1497
|
3,8801
|
3,0749
|
2,6486
|
2,3790
|
2,1906
|
2,0499
|
1,9400
|
|
72
|
6,1699
|
3,8928
|
3,0850
|
2,6572
|
2,3869
|
2,1978
|
2,0566
|
1,9464
|
|
73
|
6,1898
|
3,9053
|
3,0949
|
2,6658
|
2,3946
|
2,2049
|
2,0633
|
1,9527
|
|
74
|
6,2095
|
3,9177
|
3,1047
|
2,6743
|
2,4021
|
2,2119
|
2,0698
|
1,9589
|
|
75
|
6,2288
|
3,9299
|
3,1144
|
2,6826
|
2,4096
|
2,2187
|
2,0763
|
1,9650
|
|
76
|
6,2479
|
3,9420
|
3,1240
|
2,6908
|
2,4170
|
2,2256
|
2,0826
|
1,9710
|
|
77
|
6,2668
|
3,9539
|
3,1334
|
2,6990
|
2,4243
|
2,2323
|
2,0889
|
1,9770
|
|
78
|
6,2854
|
3,9656
|
3,1427
|
2,7070
|
2,4315
|
2,2389
|
2,0951
|
1,9828
|
|
79
|
6,3038
|
3,9772
|
3,1519
|
2,7149
|
2,4386
|
2,2455
|
2,1013
|
1,9886
|
|
80
|
6,3219
|
3,9887
|
3,1610
|
2,7227
|
2,4457
|
2,2519
|
2,1073
|
1,9943
|
|
81
|
6,3399
|
4,0000
|
3,1699
|
2,7304
|
2,4526
|
2,2583
|
2,1133
|
2,0000
|
|
82
|
6,3576
|
4,0112
|
3,1788
|
2,7380
|
2,4594
|
2,2646
|
2,1192
|
2,0056
|
|
83
|
6,3750
|
4,0222
|
3,1875
|
2,7456
|
2,4662
|
2,2708
|
2,1250
|
2,0111
|
|
84
|
6,3923
|
4,0331
|
3,1962
|
2,7530
|
2,4729
|
2,2770
|
2,1308
|
2,0166
|
|
85
|
6,4094
|
4,0439
|
3,2047
|
2,7604
|
2,4795
|
2,2831
|
2,1365
|
2,0219
|
|
86
|
6,4263
|
4,0545
|
3,2131
|
2,7676
|
2,4860
|
2,2891
|
2,1421
|
2,0273
|
|
87
|
6,4429
|
4,0650
|
3,2215
|
2,7748
|
2,4925
|
2,2950
|
2,1476
|
2,0325
|
|
88
|
6,4594
|
4,0754
|
3,2297
|
2,7819
|
2,4988
|
2,3009
|
2,1531
|
2,0377
|
|
89
|
6,4757
|
4,0857
|
3,2379
|
2,7889
|
2,5052
|
2,3067
|
2,1586
|
2,0429
|
|
90
|
6,4919
|
4,0959
|
3,2459
|
2,7959
|
2,5114
|
2,3124
|
2,1640
|
2,0480
|
|
91
|
6,5078
|
4,1060
|
3,2539
|
2,8028
|
2,5176
|
2,3181
|
2,1693
|
2,0530
|
|
92
|
6,5236
|
4,1159
|
3,2618
|
2,8095
|
2,5237
|
2,3237
|
2,1745
|
2,0580
|
|
93
|
6,5392
|
4,1257
|
3,2696
|
2,8163
|
2,5297
|
2,3293
|
2,1797
|
2,0629
|
|
94
|
6,5546
|
4,1355
|
3,2773
|
2,8229
|
2,5357
|
2,3348
|
2,1849
|
2,0677
|
|
95
|
6,5699
|
4,1451
|
3,2849
|
2,8295
|
2,5416
|
2,3402
|
2,1900
|
2,0726
|
|
96
|
6,5850
|
4,1546
|
3,2925
|
2,8360
|
2,5474
|
2,3456
|
2,1950
|
2,0773
|
|
97
|
6,5999
|
4,1641
|
3,3000
|
2,8424
|
2,5532
|
2,3509
|
2,2000
|
2,0820
|
|
98
|
6,6147
|
4,1734
|
3,3074
|
2,8488
|
2,5589
|
2,3562
|
2,2049
|
2,0867
|
|
99
|
6,6294
|
4,1827
|
3,3147
|
2,8551
|
2,5646
|
2,3614
|
2,2098
|
2,0913
|
