The expression is given as:

$\log_3 \left( 9 \log_3 9 \right)$

Step 1: Simplify $\log_3 9$

We know that:

$\log_3 9 = \log_3 (3^2) = 2$

Step 2: Substitute the value back into the original expression

Now, substitute $\log_3 9 = 2$ into the original expression:

$\log_3 \left( 9 \cdot 2 \right) = \log_3 (18)$

Step 3: Leave the answer in logarithmic form

Thus, the simplified expression is:

$\log_3 18$

This is the final value in logarithmic form, as it cannot be simplified further without using a calculator for an approximate value.

Would you like more details on how to calculate logarithms, or do you have any questions?

---

Here are 5 related questions:

1. What is $\log_2 16$?
2. How do you solve $\log_b (x) = y$ for $x$?
3. What is the change of base formula for logarithms?
4. Can you solve $\log_3 27$?
5. How do you calculate $\log_5 125$?

Tip: When dealing with logarithms of exponents, always try to express the number as a power of the base to simplify calculations.