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.
$ 2\log x=\log 25\qquad $... LHS: power rule
$\log x^{2}=\log 25\quad $ ... $\log $ is one-to-one
$ x^{2}=25$
$ x=\pm 5$
$ x=5\qquad $ ... satisfies (*)
$ x=-5\quad $ ... does not satisfy (*)
Thus, the solution set = $\{5\}.$
