$5^{2x - 2} = 25$ the solution set is { }.

$$5^{2x - 2} = 25$ the solution set is { }.$

$5^{2x - 2} = 25$
the solution set is { }.

Since $25 = 5^2$, the equation $5^{2x - 2}=25$ can be rewritten as $5^{2x - 2}=5^2$.

For exponential equations with the same base ($a^m=a^n$ implies $m = n$ when $a>0,a
eq1$), we have $2x - 2=2$.

Add 2 to both sides: $2x=2 + 2=4$.
Divide both sides by 2: $x=\frac{4}{2}=2$.

$\{2\}$