# Question #48746

By using change of base, ${\log}_{k} \left(m\right) = \ln \frac{m}{\ln} \left(k\right)$ and ${\log}_{m} \left(k\right) = \ln \frac{k}{\ln} \left(m\right)$.
You can see that $\ln \frac{m}{\ln} \left(k\right)$ and $\ln \frac{k}{\ln} \left(m\right)$ are reciprocals, meaning ${\log}_{k} \left(m\right)$ and ${\log}_{m} \left(k\right)$ are also reciprocals.