Question

question 1 of 10
which logarithmic equation is equivalent to the exponential equation below?
$4^c = 256$

a. $log_{256} c = 4$
b. $log_{c} 256 = 4$
c. $log_{4} c = 256$
d. $log_{4} 256 = c$

Explanation:

Step1: Recall the logarithm-exponent conversion rule

The general rule for converting an exponential equation \(a^b = c\) to a logarithmic equation is \(\log_a c = b\).

Step2: Apply the rule to the given equation

Given the exponential equation \(4^c = 256\), here \(a = 4\), \(b = c\), and \(c = 256\) (using the notation from the general rule \(a^b = c\)). Applying the conversion rule \(\log_a c = b\), we substitute the values: \(\log_4 256 = c\).

Answer:

D. \(\log_{4} 256 = c\)