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The expression you provided is \((\log a)(\log b)\).

To combine this into a single logarithm, note that \((\log a)(\log b)\) does not directly simplify using standard logarithmic properties, as the logarithm product or sum rules (such as \(\log(ab)\)) apply inside the logarithm, not when logs are multiplied together. Therefore, \((\log a)(\log b)\) cannot be rewritten as a single logarithmic expression.

The expression \((\log a)(\log b)\) remains in its current form, as no further simplification applies unless more context or additional operations are provided.

Do you have any further questions or would like additional details?

Here are 5 related questions:
1. What are the rules for combining logarithmic expressions?
2. How would the expression change if it was \(\log(ab)\) instead of \((\log a)(\log b)\)?
3. Can logarithmic functions be multiplied directly, and when would they simplify?
4. How does the logarithmic power rule \(\log(a^b)\) work?
5. What happens when logarithmic terms are divided, like \(\frac{\log a}{\log b}\)?

**Tip**: Always check for logarithmic properties like product, quotient, or power rules when simplifying logs.

Explore whether the expression (log a)(log b) can be simplified into a single logarithmic expression. This problem delves into the properties of logarithms, highlighting when product or power rules apply. Ideal for students in Grades 9-12.

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