Answer
Solution set = $\{5\}.$
Work Step by Step
For the equation to be defined, logarithms must have positive arguments
$ x \gt 0 \qquad (*)$
This is the condition eventual solutions must satisfy.
$ 3\log x=\log 125\qquad $... LHS: power rule
$\log x^{3}=\log 125\quad $ ... $\log $ is one-to-one
$ x^{3}=125$
$ x=5\qquad $ ... satisfies (*)
Thus, the solution set = $\{5\}.$
