# How do you express log_5 8 in terms of common logs?

Mar 13, 2017

${\log}_{a} x = \frac{{\log}_{b} x}{{\log}_{b} a}$
Where $b$ is the new base. We can chose a new base such as $10$ that can be easily evaluated using a normal pocket calculator.
$\frac{{\log}_{10} 8}{{\log}_{10} 5} = 1.292$