To solve \( 5 \log 125 \), we can simplify it step by step.

### Step 1: Use the multiplication rule of logarithms
The expression \( 5 \log 125 \) can be rewritten as:

\[
5 \log 125 = \log 125^5
\]

### Step 2: Simplify \( 125^5 \)
First, recognize that \( 125 = 5^3 \). So:

\[
125^5 = (5^3)^5 = 5^{15}
\]

### Step 3: Use the logarithmic property \( \log a^b = b \log a \)
Now, apply the logarithmic property:

\[
\log 5^{15} = 15 \log 5
\]

### Step 4: Final calculation
Assuming the base of the logarithm is 10 (as implied when no base is given):

\[
\log 5 \approx 0.69897
\]

Thus:

\[
15 \log 5 = 15 \times 0.69897 \approx 10.48455
\]

So, \( 5 \log 125 \approx 10.48 \).

Would you like further details on any of the steps or a deeper explanation?

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Here are five related questions:
1. How do logarithmic properties help simplify expressions?
2. What are the common logarithmic bases used in problems?
3. Can you explain the change of base formula in logarithms?
4. How does \( \log (ab) \) relate to \( \log a + \log b \)?
5. What is the derivative of a logarithmic function?

**Tip:** When solving logarithmic problems, always check for simplifications using logarithmic properties like the product, quotient, and power rules.

Solve the expression 5 log 125 by simplifying step-by-step using the power rule of logarithms. Learn how to express powers in logarithmic form and calculate using base-10 logarithms. This problem is suitable for high school students studying logarithms and exponentiation.

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