We can solve the expression \(  \log_3 54 + \log_3 18 - \log_3 12 \) using the properties of logarithms.

### Step 1: Apply the logarithm properties
The expression can be rewritten using the following properties of logarithms:
- **Product Property:** \( \log_b (xy) = \log_b x + \log_b y \)
- **Quotient Property:** \( \log_b \left(\frac{x}{y}\right) = \log_b x - \log_b y \)

Given the expression:
\[
\log_3 54 + \log_3 18 - \log_3 12
\]

### Step 2: Combine the logarithms
Using the product and quotient properties, we combine the terms:
\[
\log_3 \left(\frac{54 \times 18}{12}\right)
\]

### Step 3: Simplify the argument inside the logarithm
Now, simplify the expression inside the logarithm:
\[
\frac{54 \times 18}{12} = \frac{972}{12} = 81
\]

### Step 4: Simplify the logarithm
Now we have:
\[
\log_3 81
\]

Since \( 81 = 3^4 \), we can further simplify:
\[
\log_3 81 = \log_3 (3^4) = 4
\]

So, the final answer is:
\[
\boxed{4}
\]

Would you like more details or have any questions? Here are some related questions you might find interesting:

1. What are the properties of logarithms?
2. How do you simplify logarithmic expressions involving multiplication and division?
3. Can you solve \( \log_3 108 - \log_3 36 \)?
4. What happens when you have a logarithm with the same base and exponent?
5. How do you evaluate \( \log_3 27 \) using the properties of logarithms?
6. Can you explain the change of base formula for logarithms?
7. How would you solve \( \log_3 54 \times \log_3 18 \)?
8. What is the difference between natural logarithms and common logarithms?

**Tip:** Always remember that logarithms are exponents; they tell you the power to which you need to raise the base to get the given number.

Learn how to solve the logarithmic expression log 54 + log 18 - log 12 step-by-step using logarithm properties. This problem involves using the product and quotient properties of logarithms. Suitable for high school students.

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