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To evaluate \( \log_{64}(32) \), we need to find the power to which 64 must be raised to get 32.

### Solution:

1. **Express 64 and 32 in terms of powers of 2**:
   - \( 64 = 2^6 \)
   - \( 32 = 2^5 \)

2. Rewrite \( \log_{64}(32) \) using these powers of 2:
   \[
   \log_{64}(32) = \log_{2^6}(2^5)
   \]

3. **Use the change of base formula**:
   \[
   \log_{2^6}(2^5) = \frac{5}{6}
   \]

### Conclusion:
\[
\log_{64}(32) = \frac{5}{6}
\]

Would you like further details or have any questions?

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**Related Questions:**

1. How would you solve \( \log_{64}(16) \)?
2. What is \( \log_{8}(32) \)?
3. Can you express \( \log_{64}(1) \) and explain why?
4. How can we apply the change of base formula in general?
5. What is the value of \( \log_{125}(25) \)?

**Tip:** When working with logarithms, converting bases to powers of the same number often simplifies the calculation.

This page explains how to evaluate the logarithmic expression \( \log_{64} 32 \) using exponent rules and the change of base formula. Understand key logarithmic concepts with step-by-step solutions, ideal for high school students in Grades 9-12.

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