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The equation provided is:

\[
\log_6(2x - 8) = 2
\]

To solve this logarithmic equation, follow these steps:

### Step 1: Rewrite the logarithmic equation in exponential form
The general property of logarithms states that:

\[
\log_b(y) = x \quad \text{is equivalent to} \quad b^x = y
\]

For the equation \(\log_6(2x - 8) = 2\), this means:

\[
6^2 = 2x - 8
\]

### Step 2: Simplify the exponential equation
Since \(6^2 = 36\), the equation becomes:

\[
36 = 2x - 8
\]

### Step 3: Solve for \(x\)
Add 8 to both sides:

\[
36 + 8 = 2x
\]

\[
44 = 2x
\]

Now, divide both sides by 2:

\[
x = \frac{44}{2} = 22
\]

### Final Solution:
\[
x = 22
\]

Would you like any more details or have any questions?

### Related Questions:
1. How do you verify the solution to a logarithmic equation?
2. What are the steps for solving logarithmic equations with different bases?
3. How does changing the base in a logarithmic equation affect the solution process?
4. How do you solve logarithmic equations with multiple logarithms?
5. What are common mistakes to avoid when solving logarithmic equations?

### Tip:
Always remember to check if the argument of the logarithm is positive in the original equation, as logarithms are undefined for non-positive arguments.

Learn how to solve the logarithmic equation log₆(2x - 8) = 2 with a detailed step-by-step approach. This problem involves converting logarithmic expressions to exponential form and solving algebraically, suitable for students in Grades 9-12.

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