Home > Precalculus > Exponential and Logistic Graphs

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:

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.