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To rewrite the expression \( \log 7 + 5 \log 2 \) as a single logarithm, we can apply the logarithmic properties.

1. **Use the power rule**: The property \( a \log b = \log b^a \) allows us to rewrite \( 5 \log 2 \) as \( \log 2^5 \).
   
   So:
   \[
   \log 7 + 5 \log 2 = \log 7 + \log 32
   \]
   (since \( 2^5 = 32 \)).

2. **Use the product rule**: The property \( \log a + \log b = \log (a \times b) \) lets us combine the two logarithms:
   
   \[
   \log 7 + \log 32 = \log (7 \times 32)
   \]

3. **Simplify**:
   \[
   \log (7 \times 32) = \log 224
   \]

Thus, \( \log 7 + 5 \log 2 = \log 224 \).

If you have any more questions or need further clarification, feel free to ask!

### Related Questions:
1. How do you apply the quotient rule of logarithms?
2. What is the power rule for logarithms and how is it used?
3. Can you simplify \( \log(a) + \log(b) - \log(c) \)?
4. How do you expand \( \log(x^2y^3) \) using logarithmic properties?
5. How do you handle logarithmic expressions with different bases?

### Tip:
When working with logarithmic expressions, always look for opportunities to apply the product, quotient, or power rules for simplification.

Rewrite log 7 + 5 log 2 as a single logarithm with the same base.

Learn how to rewrite the logarithmic expression log 7 + 5 log 2 as a single logarithm using logarithmic properties such as the product and power rules. This problem is suitable for students in grades 9-11.

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