A logarithm of arbitrary base can be rewritten as the quotient of two logarithms with the same base by using the change of base formula.

This rule is valid if $a,b,$ and $c$ are positive real numbers where $b\ne 1$ and $c\ne 1.$ In particular, ${\log }_c(a)=\frac{\log (a)}{\log (c)}$ and ${\log }_c(a)=\frac{\ln (a)}{\ln (c)},$ where $\log (a)$ represents the common logarithm of $a,$ and $\ln (a)$ represents the natural logarithm of $a.$