Q 93. - Precalculus Enhanced with Graphing Utilities

Question

Solve the equation. 

$\ln e^x=5$

Step-by-Step Solution

Answer

The solution to the equation, $\ln e^x=5$ is, $x=5$.

Step 1. Given Information

The given equation to be solved is $\ln e^x=5$.

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 $\ln e^x=5$.

Use rule of change from logarithm to exponents: 

$$\begin{gathered} \ln e^x=5 \\ {e}^5=e^x \\ x=5 \end{gathered}$$

The solution to the given equation is, $x=5$.