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To expand the given logarithm expression \(\log(tu)\), we use the **product rule of logarithms**. The product rule states that:

\[
\log_b(xy) = \log_b(x) + \log_b(y)
\]

Applying this rule to \(\log(tu)\):

\[
\log(tu) = \log(t) + \log(u)
\]

This is the expanded form of the logarithm.

Would you like further details or explanations on this?

Here are five related questions for practice:

1. How would you expand \(\log(2xy)\)?
2. What happens if you need to expand \(\log(\frac{t}{u})\)?
3. Can you explain why \(\log(tu)\) expands as a sum and not a product?
4. How do you handle logarithmic expressions with exponents, such as \(\log(t^2)\)?
5. What is the general rule for expanding \(\log(tu^2)\)?

**Tip:** Remember that the logarithmic rules work best when all variables and expressions inside the logarithms are positive and well-defined.

Expand the logarithm: log(tu). Assume all expressions exist and are well-defined.

Learn how to expand the logarithmic expression log(tu) using the product rule of logarithms. This step-by-step solution demonstrates the application of the product rule and is suitable for students in Grades 9-11 studying algebra and logarithms.

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