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To solve the logarithmic expression \(\log(wv^8)\), we can expand it using logarithmic properties.

### Step-by-Step Solution:
1. **Product Rule of Logarithms**:  
   The logarithm of a product is the sum of the logarithms:
   \[
   \log(wv^8) = \log(w) + \log(v^8)
   \]

2. **Power Rule of Logarithms**:  
   The logarithm of a power can be written as a multiple of the logarithm:
   \[
   \log(v^8) = 8 \log(v)
   \]

3. **Final Expanded Expression**:  
   Substituting this into the original expression, we get:
   \[
   \log(wv^8) = \log(w) + 8 \log(v)
   \]

### Final Answer:
\[
\log(wv^8) = \log(w) + 8 \log(v)
\]

Would you like further clarification or details on any part of this solution? Here are some related questions you might find interesting:

1. How does the product rule for logarithms differ from the quotient rule?
2. Can you use the power rule to simplify \(\log((x^2y^3)^4)\)?
3. What is the change of base formula for logarithms?
4. How does the expansion change if we have \(\log(w^2 v^5)\)?
5. What happens when you apply logarithmic properties to an expression like \(\log(w/v)\)?

**Tip:** Always remember to use the product, quotient, and power rules when expanding logarithmic expressions.

Expand the logarithm: log(wv^8). Assume all expressions exist and are well-defined. Write your answer as a sum or difference of common logarithms or multiples of common logarithms. The inside of each logarithm must be a distinct constant or variable.

Learn how to expand the logarithmic expression log(wv^8) using the product and power rules of logarithms. This detailed step-by-step guide is perfect for high school students in Grades 10-12.

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