Question

In the following exercises, solve each equation.

$4^{x+2}=64$

Short answer

The answer is$x=1$

Step-by-step solution

Step 1. Given

The equation is$4^{x+2}=64$

Step 2. Solve the equation

$$\begin{gathered} 4^{x+2}=64 \\ {4}^{x+2}=4^3 \end{gathered}$$

Bases are same so the exponents should be equal.

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

Step 3. Check the answer

Put $x=1$in given equation,

$$\begin{gathered} 4^{x+2}=64 \\ {4}^{1+2}=64 \\ {4}^3=64 \\ 64=64 \end{gathered}$$

True