We can solve this expression step by step using the properties of logarithms.

Given:
\[
3 \log_5 4 + 3 \log_5 18 - 3 \log_5 13
\]

### Step 1: Factor out the 3
Since the factor of 3 is common across all terms, we can factor it out:
\[
3(\log_5 4 + \log_5 18 - \log_5 13)
\]

### Step 2: Use logarithm properties
Now, let's apply the properties of logarithms. Specifically, we'll use:

- The **addition property**: \(\log_b A + \log_b B = \log_b (A \times B)\)
- The **subtraction property**: \(\log_b A - \log_b B = \log_b \left(\frac{A}{B}\right)\)

First, apply the addition property to \(\log_5 4 + \log_5 18\):
\[
\log_5 (4 \times 18) = \log_5 72
\]

Next, apply the subtraction property to \(\log_5 72 - \log_5 13\):
\[
\log_5 \left(\frac{72}{13}\right)
\]

### Step 3: Simplify
Now, the expression simplifies to:
\[
3 \log_5 \left(\frac{72}{13}\right)
\]

This is the simplified form of the original expression. If you need the numerical value, we can proceed further with that as well.

Would you like to explore any further details or numerical evaluation?

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Here are 5 related questions to explore:

1. How do you expand logarithmic expressions with multiplication and division?
2. What are the basic properties of logarithms?
3. How do you evaluate logarithms without a calculator?
4. What are common logarithm bases (e.g., base 10, base e)?
5. How does the change of base formula work in logarithms?

**Tip:** Always check if terms can be factored out to simplify complex logarithmic expressions before expanding or simplifying.

Explore how to simplify the logarithmic expression 3log54 + 3log18 - 3log13 by using key logarithmic properties such as the addition and subtraction rules. Learn how to factor out common terms and simplify complex logarithmic equations. This detailed explanation is ideal for students in Grades 9-12.

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