The problem in the image asks for the value of:

$\log_3 81 + \log_3 \left( \frac{1}{9} \right)$

We will solve it step by step:

1. Evaluate $\log_3 81$:

   $81$ can be rewritten as $81 = 3^4$. Therefore,

   $\log_3 81 = \log_3 (3^4) = 4$

2. Evaluate $\log_3 \left( \frac{1}{9} \right)$:

   $\frac{1}{9}$ can be rewritten as $9^{-1}$, and $9 = 3^2$, so:

   $\log_3 \left( \frac{1}{9} \right) = \log_3 (3^{-2}) = -2$

3. Sum the results:

   $\log_3 81 + \log_3 \left( \frac{1}{9} \right) = 4 + (-2) = 2$

Thus, the correct answer is c. 2.

Would you like more details or have any other questions?

Here are 5 related questions to expand your understanding:

1. What is the general formula for simplifying logarithms of powers?
2. How can we simplify logarithmic expressions involving fractions?
3. What is the change of base formula in logarithms?
4. How does the logarithm of a product differ from the logarithm of a quotient?
5. Can you solve similar logarithmic problems with different bases?

Tip: To solve logarithmic problems easily, try to express the numbers in terms of powers of the base of the logarithm.