Let's break down each logarithm individually:

### 1. \( \log_5 5 \)

By definition, \( \log_b a \) means "to what power must \( b \) be raised to get \( a \)?" 

So, for \( \log_5 5 \), we are asking, "To what power must 5 be raised to get 5?"

\[
\log_5 5 = 1
\]
since \( 5^1 = 5 \).

### 2. \( \log_2 \left( \frac{1}{32} \right) \)

We need to find \( \log_2 \left( \frac{1}{32} \right) \), meaning "to what power must 2 be raised to get \( \frac{1}{32} \)?"

Notice that:
\[
32 = 2^5 \quad \text{so} \quad \frac{1}{32} = 2^{-5}
\]
Therefore:
\[
\log_2 \left( \frac{1}{32} \right) = -5
\]
since \( 2^{-5} = \frac{1}{32} \).

### Final answers:
\[
\log_5 5 = 1
\]
\[
\log_2 \left( \frac{1}{32} \right) = -5
\]

Would you like more details or have any questions?

Here are five related questions:
1. What is \( \log_b b^n \) for any base \( b \)?
2. How do you solve \( \log_2 64 \)?
3. Can you express \( \log_2 16 \) and \( \log_2 \left( \frac{1}{16} \right) \)?
4. How do you compute logarithms with non-integer bases, like \( \log_{3.5} 5 \)?
5. What is the change of base formula for logarithms?

**Tip:** Remember that \( \log_b 1 = 0 \) for any base \( b \), since \( b^0 = 1 \).

Explore how to solve logarithmic equations such as log5(5) and log2(1/32) with step-by-step explanations. This guide covers the fundamental properties of logarithms and exponents, suitable for students in Grades 9-12.

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