Answer
$x=\frac{11}{3}$
Work Step by Step
We know that if $\log_a {y}=x$ then $a^x=y$.
Hence, if $\log_3 {(3x-2)}=2$, then $3^2=3x-2$.
Solve the equation above to obtain:
\begin{align*}
9&=3x-2\\
9+2&=3x\\
11&=3x\\
x&=\frac{11}{3}\end{align*}