Is it possible to calculate logarithm without calculator and without logarithm table?

Dear all,

I would like to ask a question about calculating logarithm in base 10. Currently I'm reading an interesting book entitled: "ESSENTIALS OF PLANE TRIGONOMETRY AND ANALYTIC GEOMETRY".

The first chapter of the book is dedicated to logarithm function, its fundemantal forumlas, etc. However, I always used calculator in order to find the logarithm of a given number (base 10). In the book, there was some method (not really clear for me) presenting how to find the logarithm value of a given number based on the logarithm table.

I never managed to master the logarithm table (very complicated and ambiguous for me). Besides, after a bit googling I saw that there are different type of logarithm table (for base 10) with different number of columns and the method is not always the same.

Is there any simple method, allowing to calculate the logarithm of a number (base 10) without using a calculator and without using the logarithm table (with desired number of decimals)?

Thanks in advance,

Dariyoosh

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Re: Is it possible to calculate logarithm without calculator and without logarithm ta

Re: Is it possible to calculate logarithm without calculator and without logarithm ta

The following procedure is valid for the computation of the 'natural logaritm' of a number, i.e. the logarithm in base e. The logarithm in any other base is the 'natural logaritm' multiplied by a constant. The computation is based on the series expansion...

$\displaystyle \ln (1+x)= x -\frac{x^{2}}{2}}+ \frac{x^{3}}{3}}- \frac{x^{4}}{4}} + ... $ (1)

... which converges 'quickly enough' for $\displaystyle -.25 < x < .5$ . Now if You have to compute $\displaystyle \ln r$ with $\displaystyle r>1.5$ the procedure is...

a) devide r by 2 k times until obtain $\displaystyle \rho= \frac{r}{2^{k}}\ , \ .75< \rho < 1.5$ ...

b) set $\displaystyle x= \rho-1$ and compute with (1) $\displaystyle \ln (1+x)$ ...

c) compute $\displaystyle \ln r = \ln (1+x) + k\ \ln 2$...

Kind regards

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