Imagine you are living a lot of years ago, without calculators, slide rules, tables of logarithms, or any kind of tool but paper and pencil... how would you go about calculating log₁₀ of 2 -- or of any other number?

By the way, if your solution required calculating powers, or if you just wanted to check your solution, how would you calculate 10 to the 0.30103... power, or any other?

We would of course have to use Taylor series, Newton -Rhapson etc, sacrificing accuracy for computational time

For log x the Pade approximation of log(1+x) is x(6+x)/(6+4x)

which for x = 1 gives 0.7

the McClaurin series of log(1+x) is x-(x^2)/2 + (X^3)/3 + ...

which evaluated for 10  terms is 0.7

 

Posted by neshal on 2004-08-02 07:19:58