Q. 67 - Precalculus Enhanced with Graphing Utilities

Question

Solve the equation $2^{2x-1}=4$

and verify your results using a graphing utility.

Step-by-Step Solution

Answer

Required solution set is {1.5}. 

Step 1. Given information

$2^{2x-1}=4$

Step 2. Calculations

$$\begin{gathered} 2^{2x-1}=4 \\ {2}^{2x-1}=2^2 \\ So, 2x-1 = 2 if a^u=a^v then u=v \\ x=1.5 \end{gathered}$$

Step 3. Graphing solution

Graph $y=2^{2x-1}$ and y =4 intersect at (1.5,4)

Hence the required solution set is {1.5}.