Question

In the following exercises, solve each equation:

$2^{2x-3}=32$

Short answer

The solution of the given equation is$4.$

Step-by-step solution

Step 1. Given Information 

The given equation is$2^{2x-3}=32.$

We have to solve it.

Step 2. Solve the equation 

To solve the equation, write both sides of the equation with the same base.

So,$2^{2x-3}=2^5.$

Now, write a new equation by setting the exponents equal.

$$\begin{gathered} 2x-3=5 \\ 2x=5+3 \\ 2x=8 \\ x=4 \end{gathered}$$

Step 3. Verify the solution 

To verify the solution, substitute $x=4$in the original equation.

$$\begin{gathered} 2^{2\left(4\right)-3}=32 \\ {2}^{8-3}=32 \\ {2}^5=32 \\ 32=32 \end{gathered}$$

Hence, our result is true.