Answer
$x=\dfrac{\ln8}{2}$
Work Step by Step
Taking the natural logarithm of both sides, the given equation, $
e^{2x}=8
,$ is equivalent to
\begin{array}{l}\require{cancel}
\ln e^{2x}=\ln8
.\end{array}
Using the properties of logarithms and that $\ln e=1$, the solution to the equation above is
\begin{array}{l}\require{cancel}
2x\ln e=\ln8
\\\\
2x(1)=\ln8
\\\\
2x=\ln8
\\\\
x=\dfrac{\ln8}{2}
.\end{array}
