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To rewrite the given logarithmic equation \(\log_b 36 = 2\) in its equivalent exponential form, we use the definition of a logarithm.

The logarithmic equation \(\log_b 36 = 2\) implies that:
\[
b^2 = 36
\]
This means that \(b\) raised to the power of 2 equals 36.

Would you like a detailed explanation of how this conversion works? Here are some related questions to extend your understanding:

1. How do you convert a logarithmic equation to its exponential form in general?
2. How would you solve for \(b\) in \(b^2 = 36\)?
3. What if the base \(b\) in a logarithmic equation is unknown—how can you determine it?
4. How does the logarithmic function differ from an exponential function in terms of growth?
5. Can a logarithmic equation have a negative result? Why or why not?

**Tip:** When converting between logarithmic and exponential forms, remember that the base of the logarithm becomes the base of the exponent.

Write the equation in its equivalent exponential form: log_b 36 = 2

Learn how to convert the logarithmic equation log_b 36 = 2 to its equivalent exponential form using the definition of logarithms. This problem covers core algebraic concepts and logarithmic-exponential conversion. Suitable for students in Grades 9-12.

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