Answer
The solution is:$x=\left\{\dfrac{3}{2}\right\}$.
Work Step by Step
Since $1-5^0$, the given equation is equivalent to:
$5^{2x-3}=5^0$
Use the property $a^m = a^n \longrightarrow m=n$ to obtain:
$\begin{array}{ccc}
&2x-3&=&0
\\&2x-3+3&=&0+3
\\&2x&=&3
\\&\dfrac{2x}{2} &= &\dfrac{3}{2}
\\&x&=&\dfrac{3}{2}
\end{array}$
Thus, the solution is:$x=\left\{\dfrac{3}{2}\right\}$.
