How do I find the common logarithm of a number?

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Answer 1 · 2015-09-21T14:15:51

See the explanation.

If you have technology available for the logarithm in some other base ( $e$ or $2$ ), use

$log_10 n = log_b n / log_b 10$ (where $b = e " or "2$ )

With paper and pencil, I don't know a good series for $log_10 n$ .

Probably the simplest way is to use a series for $ln n$ and either a series or memorization for $ln 10 ~~ 2.302585093$

For $ln n$ , let $x=n-1$ and use:

$ln n = ln (1 + x) = x − x^2/2 + x^3/3- x^4/4+x^5/5- * * *$

After you find $ln n$ , use division to get $log_10 n ~~ ln n / 2.302585093$