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The given problem asks you to rewrite the logarithmic equation \(\log_5(25) = 2\) as an exponential equation using the property from Theorem 6.2, which states that:

\[
b^a = c \quad \text{if and only if} \quad \log_b(c) = a
\]

### Step-by-step solution:

You are given:

\[
\log_5(25) = 2
\]

Using the property from the theorem, \(\log_b(c) = a\) can be rewritten as \(b^a = c\).

In this case:
- \(b = 5\),
- \(a = 2\),
- \(c = 25\).

So, you can rewrite the logarithmic equation \(\log_5(25) = 2\) as the exponential equation:

\[
5^2 = 25
\]

This confirms that \(5^2 = 25\), so the rewritten exponential form is correct.

Would you like any further clarification on this, or need help with more examples?

### Related questions:
1. What is the exponential form of \(\log_3(9) = 2\)?
2. Can you convert \(\log_{10}(1000) = 3\) into exponential form?
3. How would you rewrite \(\log_7(49) = 2\) in exponential form?
4. How do you express \(\log_2(8) = 3\) as an exponential equation?
5. Can you explain why \(\log_b(1) = 0\) for any base \(b\)?

### Tip:
To convert a logarithmic equation into exponential form, remember that \(\log_b(c) = a\) is equivalent to \(b^a = c\), which can help simplify or solve many problems related to logarithms.

Rewrite log_5(25) = 2 as an exponential equation.

This problem involves converting the logarithmic equation log_5(25) = 2 into an exponential form. Learn how the relationship between logarithms and exponents can simplify such equations. Suitable for students in Grades 8-10.

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