Question

evaluating logarithmic expressions
which logarithmic equation is equivalent to $8^2 = 64$?
options:
$2 = \log_{64} 8$
$64 = \log_{2} 8$
$8 = \log_{2} 64$
$2 = \log_{8} 64$

Explanation:

Step1: Recall the logarithmic definition

The exponential equation \(a^b = c\) is equivalent to the logarithmic equation \(b=\log_{a}c\) (where \(a>0,a
eq1\)).

Step2: Analyze the given exponential equation

We are given the exponential equation \(8^{2}=64\). Here, \(a = 8\), \(b = 2\), and \(c=64\).

Step3: Convert to logarithmic form

Using the definition from Step 1, converting \(8^{2}=64\) to logarithmic form gives \(2=\log_{8}64\).

Answer:

\(2 = \log_{8}64\) (the last option among the given choices)