Question

If x satisfies the equation 4^{8x} = 256, then x is equal to .

• A. \(\frac{1}{2}\)
• B. \(\log_{16} 8\)
• C. \(\frac{2}{3}\)
• D. \(\log_4 8\)

Hint:

When solving equations with the same base, set the exponents equal to each other and solve for the variable.

Answer 1

The Correct Option is C

The given equation is:
\[ 4^{8x} = 256 \] Now, we can express both sides of the equation with base 4:
\[ 256 = 4^4 \] So the equation becomes:
\[ 4^{8x} = 4^4 \] Since the bases are the same, we can equate the exponents:
\[ 8x = 4 \] Now, solving for \(x\):
\[ x = \frac{4}{8} = \frac{1}{2} \] Thus, the value of \(x\) is \(\frac{1}{2}\), so the correct answer is (C).