The given expression is:

$\log_b(xy)$

We need to rewrite this expression in terms of the logarithms of $x$ and $y$.

Using the Product Rule for Logarithms:

The product rule states: $\log_b(mn) = \log_b(m) + \log_b(n)$

Applying the Rule:

$\log_b(xy) = \log_b(x) + \log_b(y)$

Final Expression:

$\log_b(xy) = \log_b(x) + \log_b(y)$

Would you like a detailed explanation of why this rule works or examples to practice?

Here are 5 follow-up questions for deeper understanding:

1. How would this rule change if it were $\log_b\left(\frac{x}{y}\right)$ instead of $\log_b(xy)$?
2. Can you extend this rule to three or more terms, such as $\log_b(xyz)$?
3. What is the significance of the base $b$ in logarithmic calculations?
4. How can this property help simplify logarithmic equations in problem-solving?
5. What happens if either $x$ or $y$ is equal to 1 in this expression?

Tip: Memorize key logarithmic properties like the product, quotient, and power rules—they simplify complex expressions dramatically