Answer
$b=4$
Work Step by Step
We know that if $a^x=y$, then $\log_a{y}=x$ and vice versa.
Therefore $\log_b{16}=2$ implies $b^2=16.$
Solving the equation gives:
$b^2=16\\
b^2=4^2\\$
Use the rule $a^m=b^m \longrightarrow a=b$ to obtain:
$b=4$
