Exercise 3.2.2

Prove equation (3.16)

$$ a^{\log_bc} = c^{\log_ba} $$

$$ \begin{align} a^{\log_bc} = a^{\frac{\log_ac}{\log_ab}} = \big(a^{\log_ac})^\frac{1}{\log_ab} = c^{\log_ba} \end{align} $$