Which of the following correctly uses the Product Rule of Logarithms to find an equivalent expression to log24

?(1 point)
Responses

log3⋅log8
logarithm 3 times logarithm 8

3log8
3 logarithm 8

log3+log8
logarithm 3 plus logarithm 8

log3−log8

1 answer

The Product Rule of Logarithms states that the logarithm of a product is equal to the sum of the logarithms of the factors. Mathematically, this is represented as:

\[ \log_b(m \cdot n) = \log_b(m) + \log_b(n) \]

In the case of \(\log(24)\), we can express 24 as the product of 3 and 8, since \(24 = 3 \times 8\). Therefore, using the Product Rule:

\[ \log(24) = \log(3 \cdot 8) = \log(3) + \log(8) \]

The correct response that uses the Product Rule to find an equivalent expression for \(\log(24)\) is:

log3 + log8