The question asks for the value of $\log_3 81 + \log_3 \frac{1}{9}$.

Let's solve it step by step:

1. Break down the logarithms:

   • $\log_3 81$ is the logarithm of 81 to the base 3.
   • $\log_3 \frac{1}{9}$ is the logarithm of $\frac{1}{9}$ to the base 3.

2. Simplify each term:

   • $\log_3 81$: Since $81 = 3^4$, we have: $\log_3 81 = 4$
   • $\log_3 \frac{1}{9}$: Since $\frac{1}{9} = 3^{-2}$, we have: $\log_3 \frac{1}{9} = -2$

3. Add the values: $\log_3 81 + \log_3 \frac{1}{9} = 4 + (-2) = 2$

Thus, the correct answer is $\boxed{2}$, which corresponds to option c.

Would you like further details on this solution, or any other explanations?

Here are five related questions for practice:

1. What is $\log_3 243$?
2. Simplify $\log_3 27 + \log_3 \frac{1}{3}$.
3. Solve $\log_2 16 + \log_2 \frac{1}{4}$.
4. What is $\log_5 25$?
5. Calculate $\log_4 64$.

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