Solve the exponential equation.
$4^{x+7}=16$

• A. $2$
• B. $5$
• C. $9$
• D. $-5$

Answer: (D)

Verified step by step guidance

1. First, identify the structure of the exponential equation. The equation given is \( 4^{x+7} = 16 \).
2. Recognize that 16 can be expressed as a power of 4. Specifically, \( 16 = 4^2 \). This allows us to rewrite the equation as \( 4^{x+7} = 4^2 \).
3. Since the bases are the same, you can set the exponents equal to each other. This gives us the equation \( x+7 = 2 \).
4. Solve for \( x \) by isolating it on one side of the equation. Subtract 7 from both sides to get \( x = 2 - 7 \).
5. Simplify the expression to find the value of \( x \). This results in \( x = -5 \).