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.