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

### Step 1: Understand the natural logarithm equation
The natural logarithm function \( \ln(y) \) equals 0 when \( y = 1 \). This is because \( \ln(1) = 0 \).

### Step 2: Set up the equation
Given the equation \( \ln(x - 2) = 0 \), set the argument of the logarithm equal to 1:
\[
x - 2 = 1
\]

### Step 3: Solve for \( x \)
Now, solve the equation for \( x \):
\[
x = 1 + 2
\]
\[
x = 3
\]

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

Would you like any details or further explanations? 

Here are 5 related questions you might find useful:
1. How do you solve natural logarithm equations with different bases?
2. What is the domain of the natural logarithm function?
3. How do you solve \( \ln(x) = a \) for \( x \)?
4. What is the difference between natural logarithms and common logarithms?
5. How do you differentiate \( \ln(x) \) with respect to \( x \)?

**Tip:** Always check the domain of the logarithm function to ensure that the arguments are within valid ranges.

Learn how to solve the natural logarithm equation ln(x - 2) = 0 step-by-step. This problem involves understanding logarithmic functions and their properties, specifically the natural logarithm. Suitable for high school students studying advanced algebra.

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