Answer
$x=\frac{10}{3}.$
Work Step by Step
We know that if $a^x=y$, then $\log_a {y}=x$ and vice versa.
Hence $\log_3{(3x-1)}=2$ implies $3x-1=3^2=9.$
After adding $1$ to both sides: $3x=10$.
After dividing both sides by 3: $\frac{3x}{3}=x=\frac{10}{3}.$
