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.