Answer
$x=\frac{e^{2}}{2}$
Work Step by Step
We are given the equation $\ln(2x)=2$. To solve for x, remember that the base of a natural logarithm is understood to be $e$.
Therefore, $\ln(2x)=log_{e}2x=2$.
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, $2x=e^{2}$.
Divide both sides by 2.
$x=\frac{e^{2}}{2}$
