Answer
$x=\dfrac{e}{2}\approx 1.359$
Work Step by Step
Use the Product Rule to obtain:
\begin{align*}
\ln{\left(2\cdot x\right)}&=1\\
\ln{2x}&=1
\end{align*}
Recall:
$$\ln{x}=n \longrightarrow e^n=x$$
Use the definition above to obtain:
\begin{align*}
\ln{2x}&=1\\\\
e^1&=2x\\\\
e&=2x\\\\
\frac{e}{2}&=\frac{2x}{2}\\\\
\frac{e}{2}&=x\\\\
x&\approx 1.359
\end{align*}
