Q 101. - Precalculus Enhanced with Graphing Utilities

Question

Solve the equation. 

$e^{2x+5}=8$

Step-by-Step Solution

Answer

The solution to the equation, $e^{2x+5}=8$is, $x=\frac{1}{2}(\ln 8-5)$.

Step 1. Given Information

The given equation to be solved is $e^{2x+5}=8$.

Step 2. Formula used

Natural logarithm:

$\ln e=1$

Step 3. Finding Solution

The given equation is $e^{2x+5}=8$.

Take logarithm on both sides.

$$\begin{gathered} e^{2x+5}=\ln 8 \\ (2x+5)\ln e=\ln 8 \\ 2x+5=\ln 8 \\ 2x=\ln 8-5 \\ x=\frac{1}{2}(\ln 8-5) \end{gathered}$$

The solution to the given equation is,  $x=\frac{1}{2}(\ln 8-5)$.