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The problem asks to evaluate \( \log_9 81 \).

This means we are trying to find the exponent \( x \) such that:

\[
9^x = 81
\]

First, express both 9 and 81 as powers of a common base. We know that:

\[
9 = 3^2 \quad \text{and} \quad 81 = 3^4
\]

So the equation becomes:

\[
(3^2)^x = 3^4
\]

Simplify the left-hand side:

\[
3^{2x} = 3^4
\]

Since the bases are the same, we can equate the exponents:

\[
2x = 4
\]

Solve for \( x \):

\[
x = \frac{4}{2} = 2
\]

Thus, \( \log_9 81 = 2 \).

The correct answer is **2**.

Would you like further clarification, or do you have any other questions?

Here are 5 related questions for further practice:
1. Evaluate \( \log_3 81 \).
2. Solve \( \log_5 25 \).
3. What is \( \log_4 16 \)?
4. Find the value of \( \log_7 49 \).
5. Solve \( \log_2 32 \).

**Tip**: When evaluating logarithms, try to express both the base and the number as powers of the same base for easier calculation.

Learn how to evaluate the logarithm log_9 81 with a detailed explanation. Understand the key concepts of logarithms and exponential functions. Suitable for students in Grades 9-10.

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