Answer
$x=5$
Work Step by Step
RECALL:
$a \cdot \log_b{x} = \log_b{(x^a)}$
Use the rule above to obtain:
$\log{(x^2)}=\log{25}$
Use the rule "$\log_b{a} =\log_b{c} \longrightarrow a = c$" to obtain:
$x^2=25$
Take the square root of both sides to obtain:
$x=\pm \sqrt{25}
\\x = \pm 5$
Note, however, that in $y=\log_b{x}$, $x \gt 0$.
This means that the solution to the given equation cannot be $-5$.
Thus, the solution to the given equation is $x=5$.
