Question

select the correct answer. which logarithmic equation correctly rewrites this exponential equation? $8^x = 64$ a. $log_{8} 64 = x$ b. $log_{8} x = 64$ c. $log_{64} 8 = x$ d. $log_{x} 64 = 8$

Explanation:

Step1: Recall exponential-logarithm conversion

For $b^y = a$, rewrite as $\log_b a = y$.

Step2: Match given equation to formula

Given $8^x = 64$, here $b=8$, $y=x$, $a=64$. Substitute into the conversion rule: $\log_8 64 = x$.

Step3: Match to option

The derived logarithmic equation matches option A.

Answer:

A. $\log_{8} 64 = x$