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To solve \(\log_9 3\), we want to determine the exponent \(x\) such that:

\[
9^x = 3
\]

We can express 9 as \(3^2\). Therefore, the equation becomes:

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

Simplifying, we have:

\[
3^{2x} = 3^1
\]

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

\[
2x = 1
\]

Solving for \(x\):

\[
x = \frac{1}{2}
\]

Thus, \(\log_9 3 = \frac{1}{2}\). The correct answer is \(\frac{1}{2}\).

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### Related Questions:
1. How do you solve logarithms with different bases?
2. What is the change of base formula in logarithms?
3. How do you evaluate \(\log_4 2\)?
4. What is the relationship between logarithms and exponents?
5. How do you simplify expressions involving logarithms?
6. What is the value of \(\log_9 81\)?
7. How do you solve logarithmic equations with multiple logarithms?
8. What are common logarithms and how are they used?

**Tip:** Remember that logarithms can be converted to a different base using the change of base formula: \(\log_b a = \frac{\log_c a}{\log_c b}\).

Learn how to solve \( \log_9 3 \) step-by-step with detailed explanations of logarithms, exponents, and the change of base formula. Suitable for Grades 10-12 students and anyone interested in logarithmic functions.

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