Answer
$x=\dfrac{11}{3}$
Work Step by Step
RECALL:
$\log_a{x} = y \longrightarrow a^y=x$
Use the definition above to obtain:
$\log_3{(3x-2)}=2
\\
\longrightarrow 3^2=3x-2
\\9=3x-2$
Add 2 on both sides of the equation to obtain:
$\begin{array}{ccc}
&9+2&= &3x-2+2
\\&11 &= &3x\end{array}$
Divide 3 on both sides of the equation to obtain:
$\frac{11}{3}=\frac{3x}{3}
\\\frac{11}{3}=x$
