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QUESTION

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

The typical graph of just ln(x) is

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

Notice the 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: