Question

solve the equation $4^{x + 1} = 64$. if no solution exists, enter none.

Explanation:

Step1: Express 64 as a power of 4

We know that \( 64 = 4^3 \), so rewrite the equation as \( 4^{x + 1}=4^3 \).

Step2: Set exponents equal

Since the bases are the same and the exponential function is one - to - one, we can set the exponents equal to each other: \( x + 1=3 \).

Step3: Solve for x

Subtract 1 from both sides of the equation: \( x=3 - 1=2 \).

Answer:

\( x = 2 \)