Question

Solve given equation and verify your result using graphing utility.

$e^{3x}=e^{2-x}$

Short answer

The solution set is$\left\{\frac{1}{2}\right\}$and it is verified through graph.

Step-by-step solution

Step 1. Given information

The given equation is :

$e^{3x}=e^{2-x}$

We have to solve for x and verify using graphing utility.

Step 2. Comparing the expressions having same bases and solving for x .

Since bases are same , therefore the exponential powers should also be the same.

$$\begin{gathered} 3x=2-x \\ 3x+x=2 \\ 4x=2 \\ x=\frac{2}{4} \\ x=\frac{1}{2} \end{gathered}$$

Step 3. Verification using graphing utility

Graph

$$\begin{gathered} Y_1=e^{3x} \\ {Y}_2=e^{2-x} \end{gathered}$$

Determine the point of intersection.

The graph intersects at $x=\frac{1}{2}$.

So the solution set is$\left\{\frac{1}{2}\right\}$.