Answer
$x=83$
Work Step by Step
We know that if $\log_a {y}=x$ then $a^x=y$.
Hence, if $\log_3 {(\sqrt{x-2})}=2$, then $\sqrt{x-2}=3^2=9$.
Square both sides both sides of the equation to obtain:
$(\sqrt{x-2})^2=9^2\\
x-2=81\\
x=81+2\\
x=81$
