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The image shows the expression \( 9 \log \sqrt{12} \). Let's break this down:

- \( \log \sqrt{12} \) can be simplified using logarithmic properties.
  
Recall that \( \log(\sqrt{a}) = \frac{1}{2} \log(a) \).

So, \( \log \sqrt{12} = \frac{1}{2} \log(12) \).

Now the full expression becomes:

\[
9 \log \sqrt{12} = 9 \times \frac{1}{2} \log(12) = \frac{9}{2} \log(12).
\]

Thus, the simplified form of the expression is:

\[
\frac{9}{2} \log(12).
\]

Would you like a further breakdown or any additional details? Here are some questions that expand on this concept:

1. What are the properties of logarithms that allow simplifying square roots?
2. How would the expression change if it was \( 9 \log(12) \) instead?
3. Can you express \( \log(12) \) in terms of smaller primes or factors?
4. What is the numerical approximation of \( \log(12) \)?
5. How do logarithmic expressions like this apply in solving real-world problems?

**Tip**: Remember, logarithmic properties, like the square root and exponent rule, can simplify many complex expressions!

Learn how to simplify the logarithmic expression 9 log(√12). This problem covers key algebraic concepts, including logarithmic properties and simplification techniques, suitable for students in Grades 9-12.

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