Q. 77 - Precalculus Enhanced with Graphing Utilities

Question

solve each equation. Verify your results using a graphing utility.

$e^x=e^{3x+8}$

Step-by-Step Solution

Answer

The value of x for which the above equation is valid is :

$-4$

Step 1. Given equation

$e^x=e^{3x+8}$

Step 2. Solving exponentially

$$\begin{gathered} e^x=e^{3x+8} \\ x=3x+8 \\ 2x=-8 \\ x=-4 \end{gathered}$$

Step 3. Verifying Graphically

Sketching the graphs of 

$e^x \& e^{3x+8}$

Where they will intersect will be the solution 

Hence verified