Question

How do you graph `ln(abs(x))`?

Answer 1

The typical graph of just `ln(x)` is

graph{ln(x) [-10, 10, -5, 5]}

Notice the domain restriction. In `ln(x)`, `x>0`. That is, negative numbers are not in the domain of a logarithmic function.

However, in `ln(abs(x))`, negative numbers are made positive.

For example, both `e^2` and `-e^2`, when plugged into `ln(abs(x))`, result in `ln(e^2)=2`.

In effect, adding the absolute value makes both the positive and negative realms available for the natural logarithm, in effect reflecting the graph over the `y`-axis, while retaining itself on the positive side: