Math Logarithms Common logarithm

Common logarithm

A special logarithm is the common logarithm or the decadic logarithm. This is the logarithm to base 10:

$\color{red}{x} = \log_{10}(a)\Leftrightarrow a=10^\color{red}{x}$


Instead of $\log_{10}$, you often write only $\log$ (or sometimes also $\lg$). Both mean the same thing.

Many calculators can calculate the logarithm only to base 10. Therefore, the following formula often helps in the calculation:

$\log_b(a) = \frac{\log(a)}{\log(b)}$


$\log_5(18)$ is not that easy to simplify and cannot be entered on some calculators.

Now use the formula, because almost every calculator should own the common logarithm.
$\log_5(18)$ $=\frac{\log(18)}{\log(5)}\approx1.7959$