Answer
$-2$
Work Step by Step
$\log_{b}x=y $ is equivalent to $ b^{y}=x.\qquad (*)$
Consequently,$\qquad \log_{b}b^{x}=x.\qquad (**)$
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$\displaystyle \frac{1}{e^{2}}=e^{-2}\quad $... (we applied a rule for exponents)
The natural logarithm is logarithm with base $ e,\quad(\ln x=\log_{e}x).$
$\displaystyle \ln\frac{1}{e^{2}}=\log_{e}e^{-2}=\quad $... apply (**)
= $-2$
