Solution 3.3:5e

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The argument of ln can be written as

\displaystyle \frac{1}{e^{2}} = e^{-2}

and with the logarithm law, \displaystyle \ln a^{b} = b\ln a, we obtain

\displaystyle \ln \frac{1}{e^{2}} = \ln e^{-2} = (-2)\cdot\ln e = (-2)\cdot 1 = -2\,\textrm{.}