Answer
$x=\frac{\ln 3}{2}$ or $x\approx 0.549$
Work Step by Step
$e^{2x}=3$ (Take the natural logarithm)
$\ln (e^{2x})=\ln 3$ (Use the property $\ln e^a=a$)
$2x=\ln 3$ (Divide by 2)
$x=\frac{\ln 3}{2}$
$x=0.5493....$
Thus, the solution is $x=\frac{\ln 3}{2}$ or $x\approx 0.549$.
