Answer
$5^{2x+1}=25$
Work Step by Step
Expressing both sides of the given equation, $
5^{2x+1}=25
,$ in the same base, the equation above is equivalent to
\begin{align*}
5^{2x+1}=5^2
.\end{align*}
Since $a^x=a^y$ implies $x=y$, the equation above implies
\begin{align*}
2x+1&=2
.\end{align*}
Using the properties of equality, the equation above is equivalent to
\begin{align*}\require{cancel}
2x+1-1&=2-1
\\
2x&=1
\\\\
\dfrac{\cancel2x}{\cancel2}&=\dfrac{1}{2}
\\\\
x&=\dfrac{1}{2}
.\end{align*}
Hence, the solution to the equation $
5^{2x+1}=25
$ is $x=\dfrac{1}{2}$.
