The question asks you to rewrite the logarithmic expression $\log_2(5xy)$ using the product property of logarithms.

The product property of logarithms states:

$\log_b(MN) = \log_b(M) + \log_b(N)$

Solution:

For $\log_2(5xy)$, treat $5xy$ as the product of three terms: $5$, $x$, and $y$.

Using the product property:

$\log_2(5xy) = \log_2(5) + \log_2(x) + \log_2(y)$

This is the simplified expression as a sum of logarithms.

Would you like further clarification or examples? Here are 5 questions to deepen your understanding:

1. What is the product property of logarithms, and how does it simplify expressions?
2. How do you handle logarithms with division (quotient property)?
3. What happens when you combine logarithms with different bases?
4. How can this rule be applied to logarithmic equations in real-world scenarios?
5. How do logarithmic properties relate to exponents?

Tip: Always break down complex logarithmic expressions step by step using the appropriate property (product, quotient, or power).