How do I find the common logarithm of a number?

Question

15149 views around the world

You can reuse this answer
Creative Commons License

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#