Making a Logarithm Table
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A logarithm table is made from an arithmetic sequence, generated by repeatedly adding a number,
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paired with a geometric sequence, generated by repeatedly multiplying a number.
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This spreadsheet starts by adding by 1's (column A) and multiplying by 10s (column B).
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Then the sequences are split halfway in between.
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"Halfway between" for addition is the average, or mean: add, then divide by 2.
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"Halfway between" for multiplication is the geometric mean: multiply, then take the square root.
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The result is more detailed arithmetic and geometric sequences containing the first ones.
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See the second tab, below, for how to use logarithm tables for calculations.
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See the website Mathematical Intentions for a more complete explanation:
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1 split2 splits3 splits4 splits5 splits4 splits5 splits6 splits
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Multiplying column
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(arithmetic sequence)
(geometric sequence)
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Increment:Factor:Increment:Factor:Increment:Factor:Increment:Factor:Increment:Factor:Increment:Factor:Increment:Factor:Increment:Factor:Increment:Factor:
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1100.53.162277660.251.778279410.1251.3335214320.06251.1547819850.031251.0746078280.0156251.0366329280.00781251.0181517220.003906251.009035045
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18
010101010101010101
19
1100.53.162277660.251.778279410.1251.3335214320.06251.1547819850.031251.0746078280.0156251.0366329280.00781251.0181517220.003906251.009035045
20
21001100.53.162277660.251.778279410.1251.3335214320.06251.1547819850.031251.0746078280.0156251.0366329280.00781251.018151722
21
310001.531.62277660.755.6234132520.3752.3713737060.18751.5399265260.093751.2409377610.0468751.113973860.02343751.0554496010.011718751.027350768
22
41000021001100.53.162277660.251.778279410.1251.3335214320.06251.1547819850.031251.0746078280.0156251.036632928
23
51000002.5316.2277661.2517.78279410.6254.2169650340.31252.0535250260.156251.433012570.0781251.197085030.03906251.0941138110.019531251.045998953
24
61000000310001.531.62277660.755.6234132520.3752.3713737060.18751.5399265260.093751.2409377610.0468751.113973860.02343751.055449601
25
7100000003.53162.277661.7556.234132520.8757.4989420930.43752.7384196340.218751.65481710.1093751.2863969450.05468751.1341944040.027343751.064985635
26
810000000041000021001100.53.162277660.251.778279410.1251.3335214320.06251.1547819850.031251.074607828
27
910000000002.25177.8279411.12513.335214320.56253.6517412730.281251.9109529750.1406251.3823722270.07031251.1757432660.035156251.084316958
28
10100000000002.5316.2277661.2517.78279410.6254.2169650340.31252.0535250260.156251.433012570.0781251.197085030.03906251.094113811
29
111000000000002.75562.34132521.37523.713737060.68754.8696752520.343752.2067340690.1718751.4855080170.08593751.2188141850.042968751.103999178
30
121000000000000310001.531.62277660.755.6234132520.3752.3713737060.18751.5399265260.093751.2409377610.0468751.11397386
31
13100000000000003.251778.279411.62542.169650340.81256.4938163160.406252.5482967480.2031251.5963385440.10156251.2634629180.050781251.124038664
32
141000000000000003.53162.277661.7556.234132520.8757.4989420930.43752.7384196340.218751.65481710.1093751.2863969450.05468751.134194404
33
151E+153.755623.4132521.87574.989420930.93758.6596432340.468752.9427271760.2343751.7154378960.11718751.3097472640.058593751.144441901
34
41000021001100.53.162277660.251.778279410.1251.3335214320.06251.154781985
35
2.125133.35214320.531253.3982083290.2656251.8434229920.13281251.3577271420.066406251.165215492
36
2.25177.8279410.56253.6517412730.281251.9109529750.1406251.3823722270.07031251.175743266
37
2.375237.13737060.593753.9241897580.2968751.9809567790.14843751.4074646630.074218751.186366159
38
2.5316.2277660.6254.2169650340.31252.0535250260.156251.433012570.0781251.19708503
39
2.625421.69650340.656254.5315836380.3281252.1287516620.16406251.4590242160.082031251.207900747
40
2.75562.34132520.68754.8696752520.343752.2067340690.1718751.4855080170.08593751.218814185
41
2.875749.89420930.718755.2329911470.3593752.28757320.17968751.5124725450.089843751.229826226
42
310000.755.6234132520.3752.3713737060.18751.5399265260.093751.240937761
43
3.1251333.5214320.781256.0429639020.3906252.4582440690.19531251.5678788440.097656251.252149689
44
3.251778.279410.81256.4938163160.406252.5482967480.2031251.5963385440.10156251.263462918
45
3.3752371.3737060.843756.9783058490.4218752.641648320.21093751.6253148370.105468751.274878362
46
3.53162.277660.8757.4989420930.43752.7384196340.218751.65481710.1093751.286396945
47
3.6254216.9650340.906258.0584218780.4531252.8387359650.22656251.6848548790.113281251.298019599
48
3.755623.4132520.93758.6596432340.468752.9427271760.2343751.7154378960.11718751.309747264
49
3.8757498.9420930.968759.3057204090.4843753.050527890.24218751.7465760480.121093751.32158089
50
4100001100.53.162277660.251.778279410.1251.333521432
51
0.5156253.2781211510.25781251.8105582430.128906251.345569858
52
0.531253.3982083290.2656251.8434229920.13281251.357727142
53
0.5468753.5226946510.27343751.8768842940.136718751.369994268
54
0.56253.6517412730.281251.9109529750.1406251.382372227
55
0.5781253.7855152490.28906251.9456400620.144531251.394862022
56
0.593753.9241897580.2968751.9809567790.14843751.407464663
57
0.6093754.0679443210.30468752.0169145550.152343751.42018117
58
0.6254.2169650340.31252.0535250260.156251.43301257
59
0.6406254.3714448130.32031252.0908000410.160156251.445959903
60
0.656254.5315836380.3281252.1287516620.16406251.459024216
61
0.6718754.6975888170.33593752.167392170.167968751.472206565
62
0.68754.8696752520.343752.2067340690.1718751.485508017
63
0.7031255.0480657170.35156252.2467900920.175781251.498929649
64
0.718755.2329911470.3593752.28757320.17968751.512472545
65
0.7343755.4246909370.36718752.3290965920.183593751.526137803
66
0.755.6234132520.3752.3713737060.18751.539926526
67
0.7656255.8294153470.38281252.4144182210.191406251.553839831
68
0.781256.0429639020.3906252.4582440690.19531251.567878844
69
0.7968756.2643353670.39843752.5028654310.199218751.582044699
70
0.81256.4938163160.406252.5482967480.2031251.596338544
71
0.8281256.7317038240.41406252.5945527210.207031251.610761535
72
0.843756.9783058490.4218752.641648320.21093751.625314837
73
0.8593757.2339416270.42968752.6895987860.214843751.63999963
74
0.8757.4989420930.43752.7384196340.218751.6548171
75
0.8906257.7736503020.44531252.7881266650.222656251.669768447
76
0.906258.0584218780.4531252.8387359650.22656251.684854879
77
0.9218758.353625470.46093752.890263910.230468751.700077619
78
0.93758.6596432340.468752.9427271760.2343751.715437896
79
0.9531258.9768713240.47656252.9961427410.238281251.730936955
80
0.968759.3057204090.4843753.050527890.24218751.746576048
81
0.9843759.6466161990.49218753.1059002240.246093751.762356441
82
1100.53.162277660.251.77827941
83
0.50781253.2196784440.253906251.794346244
84
0.5156253.2781211510.25781251.810558243
85
0.52343753.3376246940.261718751.826916718
86
0.531253.3982083290.2656251.843422992
87
0.53906253.4598916610.269531251.860078402
88
0.5468753.5226946510.27343751.876884294
89
0.55468753.5866376240.277343751.893842027
90
0.56253.6517412730.281251.910952975
91
0.57031253.7180266640.285156251.928218521
92
0.5781253.7855152490.28906251.945640062
93
0.58593753.8542288690.292968751.963219007
94
0.593753.9241897580.2968751.980956779
95
0.60156253.9954205590.300781251.998854812
96
0.6093754.0679443210.30468752.016914555
97
0.61718754.1417845140.308593752.035137468
98
0.6254.2169650340.31252.053525026
99
0.63281254.293510210.316406252.072078717
100
0.6406254.3714448130.32031252.090800041