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To rewrite the given expression \( \log 2 - \log 9 \) as a single logarithm, we can apply the **logarithmic subtraction rule**:

\[
\log_b(a) - \log_b(c) = \log_b\left(\frac{a}{c}\right)
\]

For the expression \( \log 2 - \log 9 \), we apply the rule:

\[
\log \left(\frac{2}{9}\right)
\]

Thus, the expression simplifies to:

\[
\log \frac{2}{9}
\]

Would you like further details on this topic? Here are five related questions:

1. How do you combine multiple logarithmic expressions into a single logarithm?
2. What happens when you add two logarithms with the same base?
3. How can the properties of logarithms simplify complex logarithmic expressions?
4. What is the reverse process of combining logarithms (expanding)?
5. How do you apply logarithms to solve exponential equations?

**Tip:** Always remember to check the base of the logarithms before combining them!

Rewrite the logarithmic expression as a single logarithm with the same base: log 2 - log 9

Learn how to rewrite the logarithmic expression log 2 - log 9 as a single logarithm using the logarithmic subtraction rule. This problem demonstrates the concept of logarithmic properties and simplification, suitable for high school students in Grades 9-12.

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