Answer
$x=\dfrac{\ln8}{3}\approx 0.6931$
Work Step by Step
Divide $2$ to both sides to obtain:
$$e^{3x}=8$$
Take the natural logarithm of both sides to obtain:
\begin{align*}
\ln{\left(e^{3x}\right)}&=\ln{8}\\\\
\end{align*}
Use the Power Rule of logarithms to obtain:
\begin{align*}
(3x)\ln{e}&=\ln{8}\\\\
\end{align*}
Use the rule $\ln{e}=1$ to obtain:
\begin{align*}
3x(1)&=\ln8\\\\
3x&=\ln8\\\\
\frac{3x}{3}&=\frac{\ln8}{3}\\\\
x&=\frac{\ln8}{3}\\\\
x&\approx 0.6931
\end{align*}
