Answer
The solution is $x=\left\{1\right\}$.
Work Step by Step
Since $\dfrac{1}{10}=10^{-1}$, then the given equation is equivalent to:
$10^{2x-3}=10^{-1}$
Use the property $a^m = a^n \longrightarrow m=n$ to obtain:
$\begin{array}{ccc}
&2x-3&=&-1
\\&2x-3+3&=&-1+3
\\&2x&=&2
\\&\dfrac{2x}{2} &= &\dfrac{2}{2}
\\&x&=&1
\end{array}$
Thus, the solution is $x=\left\{1\right\}$.
