Answer
$\dfrac{10}{3}$
Work Step by Step
The domain of the variable requires that $3x-1>0$.
Thus,
$3x>1\\
x>\dfrac{1}{3}$
Recall:
$y = \log_a b \text{ is equivalent to } b=a^y$.
Therefore,
$\log_3 (3x-1) = 2 \text{ is equivalent to } 3x-1 = 3^2$
Solve the equation to obtain:
$3x-1 = 3^2$
$3x-1 = 9$
$3x = 9+1$
$3x=10$
$x=\boxed{\frac{10}{3}}$
