Answer
(a) $18$,
(b) $(2,18]$.
Work Step by Step
Given $f(x)=log_4(x-2)$, we have:
(a) $f(x)=2\Longrightarrow log_4(x-2)=2\Longrightarrow x-2=4^2 $, thus $x=18$, check, it fits.
(b) $f(x)\le2\Longrightarrow log_4(x-2)\le2\Longrightarrow x-2\le4^2 $, thus $x\le18$. together with domain $x\gt2$, we have the solution $(2,18]$.
