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The given problem is to rewrite the exponential equation as a logarithmic equation using the property \( b^a = c \) if and only if \( \log_b(c) = a \).

### Problem:
\[
\left(\frac{1}{3}\right)^{-2} = 9
\]

### Solution:
1. **Rewrite the exponential form as a logarithmic equation:**

   The given equation is of the form \( b^a = c \), where:
   - \( b = \frac{1}{3} \)
   - \( a = -2 \)
   - \( c = 9 \)

   Using the property, we can rewrite this as:
   \[
   \log_{\frac{1}{3}}(9) = -2
   \]

   This means that the logarithm with base \(\frac{1}{3}\) of 9 equals \(-2\).

Would you like more details or have any questions about this? Here are some related questions to explore further:

1. What is the general method to convert any exponential equation into a logarithmic equation?
2. How do you solve logarithmic equations when given in this form?
3. What are the properties of logarithms with fractional bases?
4. How can we verify the solution by calculating \(\left(\frac{1}{3}\right)^{-2}\)?
5. How does the change of base formula apply to \(\log_{\frac{1}{3}}(9)\)?

**Tip:** Remember that a negative exponent indicates a reciprocal. For example, \(\left(\frac{1}{3}\right)^{-2}\) equals \(3^2\).

(1/3)^(-2) = 9. Rewrite the given exponential equation in logarithmic form using the property b^a = c if and only if log_b(c) = a.

Learn how to convert the exponential equation (1/3)^(-2) = 9 into a logarithmic form using the property b^a = c if and only if log_b(c) = a. This problem involves key algebraic concepts, including exponential and logarithmic relationships. Suitable for high school students in Grades 9-12.

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