Answer
$\ln{x}-x$
Work Step by Step
Recall:
$\log_a{\left(\dfrac{M}{N}\right)} = \log_a M-\log_a N$
Using the rule above gives:
$\ln \left(\dfrac{x}{e^x} \right) = \ln{x}-\ln{\left(e^x\right)}$
Recall also that $\ln e^x = x$.
Thus,
$\ln{\left(\dfrac{x}{e^x} \right)} = \boxed{\ln{x}-x}$
