Final Answer:
The product property of logarithms states that the logarithm of a product is equal to the sum of the logarithms of the individual factors. In other words, if a and b are positive numbers and b ≠ 1, then log(ab) = log(a) + log(b).
Step-by-step explanation:
To expand a logarithmic expression using the product property, follow these steps:
Identify the product of factors within the logarithmic expression. For instance, in the expression log(xy^2), xy^2 is the product of factors.
Using the product property, rewrite the logarithmic expression as the sum of individual logarithms:
log(xy^2) = log(x) + log(y^2)
Simplify the expression by applying the power property of logarithms if necessary. For example, in the expression log(y^2), the power property states that log(a^n) = n · log(a), so log(y^2) can be rewritten as 2 · log(y).
Combine the simplified expressions to obtain the expanded logarithmic expression:
log(xy^2) = log(x) + 2 · log(y)