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The function given is \( f(x) = \ln(|x - 6|) \). To find the discontinuities of this function, we need to identify where the function is undefined. The natural logarithm function \( \ln(y) \) is defined only for \( y > 0 \).

Here, the argument of the logarithm function is \( |x - 6| \). The absolute value \( |x - 6| \) equals zero when \( x = 6 \). At \( x = 6 \), the function \( \ln(|x - 6|) \) becomes \( \ln(0) \), which is undefined. 

Therefore, there is a discontinuity at \( x = 6 \). This is a point discontinuity, specifically a jump discontinuity, because the function jumps from \( +\infty \) on the immediate left of 6 to \( -\infty \) on the immediate right, or vice versa, depending on the direction of approach.

### Further Questions:
1. Would you like to see the graph of the function to visualize the discontinuity?
2. Do you need to find any other properties of this function, like its domain or range?
3. Can I help with finding the derivative of this function?
4. Are there any limits involving this function that you would like to calculate?
5. Would you like a more detailed explanation of why \( \ln(0) \) is undefined?

### Tip:
When examining functions with logarithms, always first look at the domain restrictions imposed by the logarithmic function, which requires positive arguments.

Consider the function f(x) = ln(|x - 6|). Where are the discontinuities located?

Explore where the function f(x) = ln(|x - 6|) has discontinuities and why the logarithm becomes undefined at x = 6. This example demonstrates how to analyze discontinuities in logarithmic functions involving absolute values.

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