We are given the expression:

\[
\log_3{27} + \log_3{6} - \log_3{2}
\]

Let's simplify this step by step.

### Step 1: Simplify \(\log_3{27}\)
Since \(27 = 3^3\), we can simplify:

\[
\log_3{27} = 3
\]

### Step 2: Apply the logarithmic property for addition
We can combine the logarithms \(\log_3{6}\) and \(-\log_3{2}\) using the logarithmic property:

\[
\log_b{x} - \log_b{y} = \log_b{\left(\frac{x}{y}\right)}
\]

So,

\[
\log_3{6} - \log_3{2} = \log_3{\left(\frac{6}{2}\right)} = \log_3{3}
\]

### Step 3: Simplify \(\log_3{3}\)
Since \(\log_3{3} = 1\), we can now simplify the expression:

\[
\log_3{6} - \log_3{2} = 1
\]

### Step 4: Final calculation
Now we add the two simplified terms:

\[
\log_3{27} + (\log_3{6} - \log_3{2}) = 3 + 1 = 4
\]

Thus, the simplified value of the expression is:

\[
\boxed{4}
\]

Would you like more details or have any questions?

Here are 5 related questions you might find helpful:
1. How do logarithmic addition and subtraction rules work in general?
2. What is the change of base formula for logarithms?
3. How do you solve equations involving logarithms and exponents?
4. Can you express \(\log_b{a^x}\) in simpler terms?
5. How do logarithms relate to exponential growth and decay?

**Tip:** When simplifying logarithmic

Learn how to simplify the logarithmic expression log_3(27) + log_3(6) - log_3(2) step by step. This problem covers key logarithmic concepts such as the logarithmic identity and properties of logarithms. Suitable for high school students in Grades 10-12.

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