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To solve the equation \( \log_8 32 + \log_8 2 \):

### Step-by-Step Solution

1. **Combine the Logarithmic Terms**:
   Since we are adding two logarithms with the same base, we can use the property:
   \[
   \log_b x + \log_b y = \log_b (x \cdot y)
   \]
   Therefore:
   \[
   \log_8 32 + \log_8 2 = \log_8 (32 \cdot 2) = \log_8 64
   \]

2. **Evaluate \( \log_8 64 \)**:
   Now, we need to find the value of \( \log_8 64 \). This represents the power to which 8 must be raised to get 64:
   \[
   8^2 = 64
   \]
   Thus, \( \log_8 64 = 2 \).

### Final Answer
The value of the equation is **2**.

Would you like more details or have any questions?

Here are some additional related questions for further exploration:

1. How would the solution change if the base of the logarithms was different, such as base 4 or 10?
2. What if we had to evaluate \( \log_8 16 + \log_8 2 \)? How would you approach that?
3. How does the change of base formula help in solving logarithmic equations?
4. Can you find \( \log_8 (32 \div 2) \) and verify if it gives the expected result?
5. How would you solve \( \log_b x = n \) if the base \( b \) and result \( n \) are known?

**Tip**: Remember that adding logarithms with the same base simplifies to the logarithm of the product. This property is useful for combining terms in logarithmic expressions.

Find the value of the equation \( \log_8 32 + \log_8 2 \)

Learn how to solve the logarithmic expression \( \log_8 32 + \log_8 2 \) using properties of logarithms. This problem demonstrates how to combine logarithmic terms with the same base and evaluate the result.

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