# How do you use the Change of Base Formula and a calculator to evaluate the logarithm log_6 120?

Some scientific calculators allow you to choose the base of the logarithm. However, if this is not the case, then the log function needs to be represented in terms of either base $10$ or base $e$.
${\log}_{a} b = {\log}_{c} \frac{b}{\log} _ c a$
Hence: ${\log}_{6} 120 = {\log}_{10} \frac{120}{\log} _ 10 6 = \ln \frac{120}{\ln} 6$
where $\ln$ is the natural logarithm i.e. ${\log}_{e}$