Solution

Solve for $b$ in the following:

$$\displaystyle{\log_b 16 = \frac{4}{3}}$$


$$\begin{array}{rcll} \log_b 16 &=& \frac{4}{3} & \scriptsize{\textrm{Being the base, } b \textrm{ is in an awkward spot -- rewriting things in exponential form can help...}}\\\\ b^{4/3} &=& 16 & \scriptsize{\textrm{From here, we just undo the exponentiation by raising both sides to the } 3/4 \textrm{ power}}\\\\ b &=& 16^{3/4}\\\\ b &=& 8 \end{array}$$