Answer
$x=\frac{e^{-1}+3}{2}$
Work Step by Step
We are given the equation $\ln(2x-3)=-1$. To solve for x, remember that the base of a natural logarithm is understood to be $e$.
Therefore, $\ln(2x-3)=log_{e}(2x-3)=-1$.
If $b\gt0$ and $b\ne1$, then $y=log_{b}x$ means $x=b^{y}$ for every $x\gt0$ and every real number $y$.
Therefore, $2x-3=e^{-1}$.
Add 3 to both sides.
$2x=e^{-1}+3$
Divide both sides by 2.
$x=\frac{e^{-1}+3}{2}$
