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How to calculate the common logartithm found in the logarithm tables? How to use Taylor series expansion calculation for the logarithm function ? I am specifically interested in writing an algorithm for generating the logarithm tables.

I am a Physics teacher at the sophomore level.

ln(x) = 2 Sum(k=1,inf)(1/(2k-1))((x-1)/(x+1))^2k-1

Then use change of base formula to convert to base 10.

For reference see *Table of Integrals, Series and Products* by I.S. Gradshteyn and I.M. Ryzhik (Academic Press)


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