To solve the equation $\ln(x - 2) = 0$, we can follow these steps:

Step 1: Understand the logarithmic equation

The equation given is $\ln(x - 2) = 0$. This means that the natural logarithm (logarithm base $e$) of $x - 2$ equals 0.

Step 2: Solve for $x - 2$

Recall that $\ln(y) = 0$ implies $y = 1$. This is because $\ln(1) = 0$.

So, we set $x - 2 = 1$.

Step 3: Solve for $x$

Now, add 2 to both sides of the equation:

$x - 2 = 1$

$x = 1 + 2$

$x = 3$

Final Answer:

The solution to the equation $\ln(x - 2) = 0$ is $x = 3$.

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Would you like more details or have any questions? Here are some related questions:

1. What are the properties of the natural logarithm function?
2. How do you solve logarithmic equations in general?
3. What happens if the logarithm is defined with a different base?
4. How do you solve equations involving multiple logarithmic terms?
5. What is the domain of the function $\ln(x - 2)$?

Tip: Always check the domain of the logarithmic function to ensure that the argument is positive before solving the equation.