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The problem consists of two logarithmic expressions that need to be evaluated.

### (a) \( \log_6 36 \)

We want to find \( \log_6 36 \), which is asking, "What power must 6 be raised to in order to get 36?"

Since:
\[
6^2 = 36
\]
We have:
\[
\log_6 36 = 2
\]

### (b) \( \log_8 \frac{1}{64} \)

This asks for the logarithm base 8 of \( \frac{1}{64} \), i.e., "What power must 8 be raised to in order to get \( \frac{1}{64} \)?"

We know:
\[
8^2 = 64 \quad \text{so} \quad 8^{-2} = \frac{1}{64}
\]
Therefore:
\[
\log_8 \frac{1}{64} = -2
\]

### Final Answers:
- (a) \( \log_6 36 = 2 \)
- (b) \( \log_8 \frac{1}{64} = -2 \)

Would you like further details or have any questions?

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Here are 5 related questions for further exploration:
1. How do you solve logarithmic equations with different bases?
2. What are the properties of logarithms that can simplify their evaluation?
3. How would you express \( \log_b 1 \) for any base \( b \)?
4. Can logarithmic expressions with different bases be easily converted into a single base?
5. How do logarithms relate to exponential functions?

**Tip:** Always remember that \( \log_b b^x = x \).

Evaluate the logarithmic expressions: (a) log_6(36) and (b) log_8(1/64)

Learn how to evaluate the logarithmic expressions log_6(36) and log_8(1/64) using exponent properties. Understand key logarithmic concepts, formulas, and their applications. Ideal for students in Grades 9-11.

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