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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Adding column
Multiplying column
AddingMultiplyingAddingMultiplyingAddingMultiplyingAddingMultiplyingAddingMultiplyingAddingMultiplyingAddingMultiplyingAddingMultiplying
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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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010101010101010101
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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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21001100.53.162277660.251.778279410.1251.3335214320.06251.1547819850.031251.0746078280.0156251.0366329280.00781251.018151722
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310001.531.62277660.755.6234132520.3752.3713737060.18751.5399265260.093751.2409377610.0468751.113973860.02343751.0554496010.011718751.027350768
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41000021001100.53.162277660.251.778279410.1251.3335214320.06251.1547819850.031251.0746078280.0156251.036632928
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51000002.5316.2277661.2517.78279410.6254.2169650340.31252.0535250260.156251.433012570.0781251.197085030.03906251.0941138110.019531251.045998953
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61000000310001.531.62277660.755.6234132520.3752.3713737060.18751.5399265260.093751.2409377610.0468751.113973860.02343751.055449601
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7100000003.53162.277661.7556.234132520.8757.4989420930.43752.7384196340.218751.65481710.1093751.2863969450.05468751.1341944040.027343751.064985635
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810000000041000021001100.53.162277660.251.778279410.1251.3335214320.06251.1547819850.031251.074607828
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910000000002.25177.8279411.12513.335214320.56253.6517412730.281251.9109529750.1406251.3823722270.07031251.1757432660.035156251.084316958
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10100000000002.5316.2277661.2517.78279410.6254.2169650340.31252.0535250260.156251.433012570.0781251.197085030.03906251.094113811
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111000000000002.75562.34132521.37523.713737060.68754.8696752520.343752.2067340690.1718751.4855080170.08593751.2188141850.042968751.103999178
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121000000000000310001.531.62277660.755.6234132520.3752.3713737060.18751.5399265260.093751.2409377610.0468751.11397386
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13100000000000003.251778.279411.62542.169650340.81256.4938163160.406252.5482967480.2031251.5963385440.10156251.2634629180.050781251.124038664
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141000000000000003.53162.277661.7556.234132520.8757.4989420930.43752.7384196340.218751.65481710.1093751.2863969450.05468751.134194404
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151E+153.755623.4132521.87574.989420930.93758.6596432340.468752.9427271760.2343751.7154378960.11718751.3097472640.058593751.144441901
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41000021001100.53.162277660.251.778279410.1251.3335214320.06251.154781985
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2.125133.35214320.531253.3982083290.2656251.8434229920.13281251.3577271420.066406251.165215492
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2.25177.8279410.56253.6517412730.281251.9109529750.1406251.3823722270.07031251.175743266
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2.375237.13737060.593753.9241897580.2968751.9809567790.14843751.4074646630.074218751.186366159
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2.5316.2277660.6254.2169650340.31252.0535250260.156251.433012570.0781251.19708503
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2.625421.69650340.656254.5315836380.3281252.1287516620.16406251.4590242160.082031251.207900747
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2.75562.34132520.68754.8696752520.343752.2067340690.1718751.4855080170.08593751.218814185
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2.875749.89420930.718755.2329911470.3593752.28757320.17968751.5124725450.089843751.229826226
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310000.755.6234132520.3752.3713737060.18751.5399265260.093751.240937761
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3.1251333.5214320.781256.0429639020.3906252.4582440690.19531251.5678788440.097656251.252149689
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3.251778.279410.81256.4938163160.406252.5482967480.2031251.5963385440.10156251.263462918
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3.3752371.3737060.843756.9783058490.4218752.641648320.21093751.6253148370.105468751.274878362
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3.53162.277660.8757.4989420930.43752.7384196340.218751.65481710.1093751.286396945
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3.6254216.9650340.906258.0584218780.4531252.8387359650.22656251.6848548790.113281251.298019599
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3.755623.4132520.93758.6596432340.468752.9427271760.2343751.7154378960.11718751.309747264
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3.8757498.9420930.968759.3057204090.4843753.050527890.24218751.7465760480.121093751.32158089
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4100001100.53.162277660.251.778279410.1251.333521432
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0.5156253.2781211510.25781251.8105582430.128906251.345569858
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0.531253.3982083290.2656251.8434229920.13281251.357727142
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0.5468753.5226946510.27343751.8768842940.136718751.369994268
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0.56253.6517412730.281251.9109529750.1406251.382372227
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0.5781253.7855152490.28906251.9456400620.144531251.394862022
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0.593753.9241897580.2968751.9809567790.14843751.407464663
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0.6093754.0679443210.30468752.0169145550.152343751.42018117
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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
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0.68754.8696752520.343752.2067340690.1718751.485508017
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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
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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
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0.843756.9783058490.4218752.641648320.21093751.625314837
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0.8593757.2339416270.42968752.6895987860.214843751.63999963
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0.8757.4989420930.43752.7384196340.218751.6548171
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0.8906257.7736503020.44531252.7881266650.222656251.669768447
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0.906258.0584218780.4531252.8387359650.22656251.684854879
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0.9218758.353625470.46093752.890263910.230468751.700077619
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0.93758.6596432340.468752.9427271760.2343751.715437896
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0.9531258.9768713240.47656252.9961427410.238281251.730936955
80
0.968759.3057204090.4843753.050527890.24218751.746576048
81
0.9843759.6466161990.49218753.1059002240.246093751.762356441
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1100.53.162277660.251.77827941
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0.50781253.2196784440.253906251.794346244
84
0.5156253.2781211510.25781251.810558243
85
0.52343753.3376246940.261718751.826916718
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0.531253.3982083290.2656251.843422992
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0.53906253.4598916610.269531251.860078402
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0.5468753.5226946510.27343751.876884294
89
0.55468753.5866376240.277343751.893842027
90
0.56253.6517412730.281251.910952975
91
0.57031253.7180266640.285156251.928218521
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0.5781253.7855152490.28906251.945640062
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0.58593753.8542288690.292968751.963219007
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0.593753.9241897580.2968751.980956779
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0.60156253.9954205590.300781251.998854812
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0.6093754.0679443210.30468752.016914555
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0.61718754.1417845140.308593752.035137468
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0.6254.2169650340.31252.053525026
99
0.63281254.293510210.316406252.072078717
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0.6406254.3714448130.32031252.090800041
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Logarithm tables
Calculations with log tables