Write as an exponential equation.
-$$\log _ { \mathrm { e } } \frac { 1 } { \mathrm { e } ^ { 3 } } = - 3$$
A) $\left( \frac { 1 } { e ^ { 3 } } \right) ^ { - 3 } = e$
B) $\left( \frac { 1 } { \mathrm { e } ^ { 3 } } \right) ^ { \mathrm { e } } = - 3$
C) $- 3 ^ { e } = \frac { 1 } { e ^ { 3 } }$
D) $\mathrm { e } ^ { - 3 } = \frac { 1 } { \mathrm { e } ^ { 3 } }$

Question

Quizplus · Accepted Answer

The logarithmic equation $\log_e \frac{1}{e^3} = -3$ can be rewritten in exponential form as $e^{-3} = \frac{1}{e^3}$, which matches choice D. This follows from the definition of a logarithm, where $\log_b a = c$ is equivalent to $b^c = a$.

Write as an Exponential Equation log⁡e1e3=−3\log _ { \mathrm { e } } \frac { 1 } { \mathrm { e } ^ { 3 } } = - 3loge​e31​=−3

Write as an Exponential Equation $\log _ { \mathrm { e } } \frac { 1 } { \mathrm { e } ^ { 3 } } = - 3$