Q 110. - Precalculus Enhanced with Graphing Utilities

Question

Solve the equation. 

$4e^{x+1}=5$

Step-by-Step Solution

Answer

The solution to the equation, $4e^{x+1}=5$is, $x=\ln \frac{5}{4}-1$.

Step 1. Given Information

The given equation to be solved is $4e^{x+1}=5$.

Step 2. Formula used

Natural logarithm: 

$\ln e=1$

Step 3. Finding Solution

The given equation is $4e^{x+1}=5$.

Divide both sides by$4$.

$$\begin{gathered} \frac{4e^{x+1}}{4}=\frac{5}{4} \\ {e}^{x+1}=\frac{5}{4} \end{gathered}$$

Take logarithm on both sides.

$$\begin{gathered} \ln e^{x+1}=\ln \frac{5}{4} \\ (x+1)\ln e=\ln \frac{5}{4} \\ x+1=\ln \frac{5}{4} \\ x=\ln \frac{5}{4}-1 \end{gathered}$$

The solution to the given equation is,  $x=\ln \frac{5}{4}-1$.