Question

Solve the equation.

$\ln e^{-2x}=8$

Short answer

The solution to the equation, $\ln e^{-2x}=8$is, $x=-4$.

Step-by-step solution

Step 1. Given Information

The given equation to be solved is $\ln e^{-2x}=8$.

Step 2. Formula used

Rule of change from logarithm to exponents:

$\ln b=y\Rightarrow e^y=b$

Step 3. Finding Solution

The given equation is $\ln e^{-2x}=8$.

Use rule of change from logarithm to exponents:

$$\begin{gathered} \ln e^{-2x}=8 \\ {e}^8=e^{-2x} \\ -2x=8 \\ x=-4 \end{gathered}$$

The solution to the given equationis,$x=-4$.