Answer
$1-\ln {(x)}$
Work Step by Step
Recall:
(1) $\sqrt[m]{a}=a^{\frac{1}{m}}$
(2) $\log_a {x^n}=n\cdot \log_a {x}$.
(3) $\log_a{xy}=\log_a{x} +\log_a{y}$
(4) $\log_a{\frac{x}{y}}=\log_a{x} -\log_a{y}$
(5) $\ln {e}=1$
Use Rule (4) above to obtain:
$\ln {(\frac{e}{x})}=\ln {(e)}- \ln {(x)}$
Use Rule (5) above to obtain:
$\ln {e}=1$ hence,
$\ln {(e)}- \ln {(x)}=1-\ln {(x)}$
