Answer
$x=1$
Work Step by Step
The given equation is
$\Rightarrow 5^{2x}=5^{x+1}$
Equate the exponents.
$\Rightarrow 2x=x+1$
Subtract $x$ from each side.
$\Rightarrow 2x-x=x+1-x$
Simplify.
$\Rightarrow x=1$
Check $x=1$.
$\Rightarrow 5^{2(1)}=5^{1+1}$
$\Rightarrow 5^{2}=5^{2}$
True.
