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!