Choose the one alternative that best completes the statement or answers the question.
-$$\ln \frac { 1 } { \mathrm { e } ^ { 5 } } = - 5$$
A) $\left( \frac { 1 } { \mathrm { e } ^ { 5 } } \right) ^ { - 5 } = \mathrm { e }$
B) $\left( \frac { 1 } { e ^ { 5 } } \right) ^ { e } = - 5$
C) $\mathrm { e } ^ { - 5 } = \frac { 1 } { \mathrm { e } ^ { 5 } }$
D) $- 5 ^ { \mathrm { e } } = \frac { 1 } { \mathrm { e } ^ { 5 } }$

Question

Quizplus · Accepted Answer

The logarithmic equation $\ln \frac { 1 } { \mathrm { e } ^ { 5 } } = - 5$ simplifies to $\mathrm { e } ^ { - 5 } = \frac { 1 } { \mathrm { e } ^ { 5 } }$, which is a basic property of logarithms and exponents.

Choose the One Alternative That Best Completes the Statement or Answers