Answer
(a) $x=\dfrac{1}{e}$
(b) $x=-1$
Work Step by Step
RECALL:
(1) $\ln{x}=y \longrightarrow e^y=x$
(2) $a^{-m}=\dfrac{1}{a^m}, a\ne0$
(a)
Use rule (1) above to obtain:
$\begin{array}{ccc}
&e^{-1}&=&x
\end{array}$
Use rule (2) above to obtain:
$\dfrac{1}{e}=x$
(b)
Use rule (1) above to obtain:
$\begin{array}{ccc}
&e^x&=&\dfrac{1}{e}
\end{array}$
Use the rule (2) above to obtain:
$e^x=e^{-1}$
Use the rule $a^m=a^n \longrightarrow m=n$ to obtain:
$x=-1$