Answer
$\left\{3\right\}$
Work Step by Step
Expressing both sides of the given equation, $
2^{2x-3}=8
$, in the same base results to
\begin{align*}\require{cancel}
2^{2x-3}&=2^3
.\end{align*}
Since $x^m=x^n$ implies $m=n$, the equation above implies
\begin{align*}\require{cancel}
2x-3&=3
.\end{align*}
Using the properties of equality, the equation above is equivalent to
\begin{align*}\require{cancel}
2x-3+3&=3+3
\\
2x&=6
\\\\
\dfrac{\cancel2x}{\cancel2}&=\dfrac{6}{2}
\\\\
x&=3
.\end{align*}
Hence, the solution set of the equation $
2^{2x-3}=8
$ is $
\left\{3\right\}
$.
