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, recognize that the equation is in the form of an exponential equation: \( 4^{x+7} = 16 \).
2. Notice that 16 can be rewritten as a power of 4, since \( 16 = 4^2 \).
3. Substitute \( 16 \) with \( 4^2 \) in the equation, resulting in \( 4^{x+7} = 4^2 \).
4. Since the bases are the same, you can set the exponents equal to each other: \( x+7 = 2 \).
5. Solve for \( x \) by subtracting 7 from both sides of the equation: \( x = 2 - 7 \).