Question

How do I find the common logarithm of a number?

Answer 1

See the explanation.

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`