The domain of the function \( \ln(x-6) \) is determined by the requirement that the argument of the natural logarithm (ln) must be positive. In this case, the argument is \( x - 6 \).

So, we need:
\[
x - 6 > 0
\]

To solve this inequality:
\[
x > 6
\]

Therefore, the domain of \( \ln(x-6) \) is \( x > 6 \), which in interval notation is:
\[
(6, \infty)
\]

Would you like more details on this topic or have any further questions? Here are 5 related questions that you might find interesting:

1. What is the domain of the function \( \ln(3x + 2) \)?
2. How do you find the domain of \( \sqrt{x-5} \)?
3. What is the range of the function \( \ln(x) \)?
4. How does the natural logarithm function behave as \( x \) approaches infinity?
5. What is the derivative of \( \ln(x-6) \)?

**Tip:** When working with logarithmic functions, always check that the argument inside the logarithm is positive, as the logarithm of a non-positive number is undefined.

Explore the domain of the function ln(x-6) and understand why the argument of the natural logarithm must be positive. Learn how to determine the domain using inequalities and interval notation. Suitable for Grades 11-12.

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