The Product Rule of Logarithms states that \(\log_b(m \cdot n) = \log_b(m) + \log_b(n)\). To use this rule correctly, you need to express the number 24 as a product of its prime factors or other factors.
The number 24 can be expressed as \(24 = 6 \cdot 4\), or using its prime factorization, \(24 = 2^3 \cdot 3\).
Using the prime factorization, we can apply the Product Rule:
\[ \log 24 = \log(2^3 \cdot 3) = \log(2^3) + \log(3) \]
Applying the Power Rule of Logarithms, which states \(\log_b(m^n) = n \cdot \log_b(m)\), we get:
\[ \log(2^3) = 3 \cdot \log(2) \]
Thus, the expression becomes:
\[ \log 24 = 3 \cdot \log(2) + \log(3) \]
So, the correct expression using the Product Rule of Logarithms to find an equivalent expression to \(\log 24\) is:
\[ \log 24 = 3 \cdot \log(2) + \log(3) \]
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