Answer
$1-\ln{x}$
Work Step by Step
Recall:
$\log_a\left(\dfrac{M}{N}\right) = \log_a M-\log_a N$
$\therefore \ln{\left(\dfrac{e}{x}\right)} = \ln{e}- \ln{x}$
Note that $\ln(e) = 1$.
Thus,
$\ln\left(\dfrac{e}{x}\right) = \boxed{1 - \ln{x}}$
