# How do you express log_7 5 in terms of common logs?

Nov 20, 2016

$\log \frac{5}{\log} 7$
A common log is a log to the base of 10. Logs to the base of 10 are usually simply written as $\log x$ rather than ${\log}_{10} x$, so keep that in mind for my explanation.
The change of base formula states that ${\log}_{a} b = \log \frac{b}{\log} a$.
Therefore, ${\log}_{7} 5 = \log \frac{5}{\log} 7$.