Answer
$\dfrac{1}{2}$
Work Step by Step
Since $\sqrt{e} = e^{\frac{1}{2}}$, then the given expression is equivalent to:
$$\ln{e^{\frac{1}{2}}}$$
Let
$\ln{e^{\frac{1}{2}}}=y$
Recall:
$$\ln{x} = y \longrightarrow e^y=x$$
Use the rule above to obtain:
$$\ln{e^{\frac{1}{2}}}=y \longrightarrow e^y=e^{\frac{1}{2}}$$
Using the rule $a^m=a^n\longrightarrow m=n$ gives:
$$y=\dfrac{1}{2}$$