Use Natural Logarithms
Evaluate or simplify the expression without using a calculator.
-$\ln \mathrm { e } ^ { 20 \mathrm { x } }$
A) $20 x$
B) $- 20 x$
C) $\mathrm { e } ^ { 20 \mathrm { x } }$
D) $\frac { 1 } { 20 x }$

Question

Quizplus · Accepted Answer

We know that the logarithmic function with base e (natural logarithm) is the inverse of the exponential function with base e. This means that if we take the natural logarithm of e raised to any power, the result will simply be that power.

Therefore, 
\begin{align*}
\ln \mathrm { e } ^ { 20 \mathrm { x } } &= 20x \ln \mathrm{e} \
&= 20x \cdot 1 \quad 	ext{(since }\ln \mathrm{e} = 1	ext{)} \
&= 20x
\end{align*}

Thus, the best choice is A.

Use Natural Logarithms Evaluate or Simplify the Expression Without Using ln⁡e20x\ln \mathrm { e } ^ { 20 \mathrm { x } }lne20x

Use Natural Logarithms
Evaluate or Simplify the Expression Without Using $\ln \mathrm { e } ^ { 20 \mathrm { x } }$