Answer
$x=\dfrac{\ln8}{2}\approx1.0397$
Work Step by Step
$e^{2x}=8$
Apply $\ln$ to both sides of the equation:
$\ln e^{2x}=\ln8$
Take $2x$ down to multiply in front of its respective $\ln$:
$2x\ln e=\ln8$
Since $\ln e=1$, this equation simplifies to:
$2x=\ln8$
Solve for $x$:
$x=\dfrac{\ln8}{2}\approx1.0397$