Question

In the following exercises, solve each equation.

$4^x=32$

Short answer

The answer is$x=\frac{5}{2}$

Step-by-step solution

Step 1. Given

The equation is$4^x=32$

Step 2. Solve the equation

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

Bases are same so the exponents should be equal.

$$\begin{gathered} 2x=5 \\ x=\frac{5}{2} \end{gathered}$$

Step 3. Check the answer

Put $x=\frac{5}{2}$in given equation,

$$\begin{gathered} 4^x=32 \\ {4}^{\frac{5}{2}}=32 \\ {\left(\sqrt{4}\right)}^5=32 \\ {2}^5=32 \\ 32=32 \end{gathered}$$

True