How do I find the common logarithm of a number?

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How do I find the common logarithm of a number?

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Answer 1 · 2015-09-21T14:15:51

See the explanation.

Explanation:

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

${log}_{10} n = \frac{{log}_{b} n}{{log}_{b} 10}$ $log_10 n = log_b n / log_b 10$ (where $b = e or 2$ $b = e " or "2$ )

With paper and pencil, I don't know a good series for ${log}_{10} n$ $log_10 n$ .

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

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

$ln n = ln (1 + x) = x - \frac{x^{2}}{2} + \frac{x^{3}}{3} - \frac{x^{4}}{4} + \frac{x^{5}}{5} - \cdot \cdot \cdot$ $ln n = ln (1 + x) = x − x^2/2 + x^3/3- x^4/4+x^5/5- * * *$

After you find $ln n$ $ln n$ , use division to get ${log}_{10} n \approx \frac{ln n}{2.302585093}$ $log_10 n ~~ ln n / 2.302585093$

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How do I find the common logarithm of a number?

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