$$\frac{25^{x}}{5^{2}}=5^{4} $$ $$\Rightarrow \frac{5^{2x}}{5^{2}}=5^{4} $$ $$\Rightarrow 2x-2=4 $$ $$\Rightarrow 2x=6 $$ $$\Rightarrow x=3 $$