Answer
$x\gt \dfrac{2}{3}$
or
$(\dfrac{2}{3},\infty)$
Work Step by Step
We have:
$f(x)=\log{(3x-2)}$
For $\log_a{b}$, the value of $b$ is greater than $0$ because we can not take the log of a non-positive number.
Therefore,
$3x-2\gt 0\\
3x\gt 2\\
x\gt \dfrac{2}{3}$
In other words, the domain is: $(\dfrac{2}{3},\infty)$
