Let's simplify the expression $\log_3 54 + \log_3 18 - \log_3 12$.

Using the logarithm properties, we know that:

1. $\log_b(x) + \log_b(y) = \log_b(x \cdot y)$
2. $\log_b(x) - \log_b(y) = \log_b\left(\frac{x}{y}\right)$

So, we can start by combining the first two terms:

$\log_3 54 + \log_3 18 = \log_3 (54 \cdot 18)$

Now, calculate $54 \cdot 18$:

$54 \times 18 = 972$

Thus, the expression becomes:

$\log_3 972 - \log_3 12$

Next, using the subtraction property:

$\log_3 972 - \log_3 12 = \log_3\left(\frac{972}{12}\right)$

Now, calculate $\frac{972}{12}$:

$\frac{972}{12} = 81$

So, the expression simplifies to:

$\log_3 81$

Finally, recognize that $81$ can be expressed as $3^4$:

$\log_3 81 = \log_3 (3^4) = 4$

Thus, the value of the expression is:

$\boxed{4}$

Would you like further details on this, or do you have any questions?

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