Answer
{$\frac{e^{-1}+3}{2}$}, {$1.6839$}
Work Step by Step
Step 1: $\ln (2x-3)=-1$
Step 2: $2x-3=e^{-1}$
Step 3: $2x=e^{-1}+3$
Step 4: $x=\frac{e^{-1}+3}{2}\approx1.6839$
Therefore, the exact solution is {$\frac{e^{-1}+3}{2}$}. The answer, to four decimal places, is {$1.6839$}.
