Answer
$x=\dfrac{3}{2}+\dfrac{1}{2e}\approx1.68$
Work Step by Step
$\ln(2x-3)+1=0$
Take $1$ to the right side:
$\ln(2x-3)=-1$
Rewrite this equation in exponential form:
$2x-3=e^{-1}$
Solve for $x$:
$2x-3=\dfrac{1}{e}$
$2x=3+\dfrac{1}{e}$
$x=\dfrac{3}{2}+\dfrac{1}{2e}\approx1.68$
