Answer
$x=\ln{(\frac{5}{2})}$
Work Step by Step
The given equation can be simplified as:
$$2e^x=5 \\ \implies e^x=\dfrac{5}{2}$$
Recall the exponential property that $e^{\ln a}=a$.
Take $\ln$ on both sides to obtain:
$$\ln{e^x}= \ln {\left(\frac{5}{2}\right)} \\
x=\ln{\left(\frac{5}{2}\right)}$$
