Question

solve. write your answer as an integer or a fraction in simplest form.
$4^{4x - 4} = 64$
$x = \square$

Explanation:

Step1: Express 64 as a power of 4

Since \( 64 = 4^3 \), we can rewrite the equation \( 4^{4x - 4}=64 \) as \( 4^{4x - 4}=4^3 \).

Step2: Set exponents equal (since bases are equal)

If \( a^m = a^n \) (where \( a>0,a
eq1 \)), then \( m = n \). So we have \( 4x - 4 = 3 \).

Step3: Solve for x

Add 4 to both sides: \( 4x=3 + 4=7 \). Then divide both sides by 4: \( x=\frac{7}{4} \).

Answer:

\( \frac{7}{4} \)