The equation provided in the image is:

$\log_3(6x - 3) = 2$

To solve for $x$, let's follow these steps:

Step 1: Convert the logarithmic equation to an exponential form.

The equation $\log_b(A) = C$ is equivalent to $A = b^C$. Here, $b = 3$, $A = 6x - 3$, and $C = 2$.

So, we convert: $6x - 3 = 3^2$

Step 2: Simplify the exponential expression.

$6x - 3 = 9$

Step 3: Solve for $x$.

Add 3 to both sides: $6x = 9 + 3$ $6x = 12$

Now divide by 6: $x = \frac{12}{6}$ $x = 2$

Final Answer:

$x = 2$

Would you like more details or further clarification on this? Here are some related questions to explore:

1. What are the steps to convert a logarithmic equation into an exponential form?
2. How can you solve logarithmic equations with different bases?
3. What is the general form of logarithmic and exponential equations?
4. Can you explain the properties of logarithms used to simplify more complex equations?
5. How do you solve logarithmic equations involving coefficients inside the logarithm?

Tip: When solving logarithmic equations, always check if the argument of the logarithm is positive, as the logarithm is only defined for positive values.