And I'm not going to rigorously prove it here, but I will give you kind of the conceptual understanding. So to understand it, let's plot the natural log of x. And I had done this ahead of time. So that right over there is roughly what the graph of the natural log of x looks like. So what would the natural log of the absolute value of x is going to look like? Well, for positive x's, it's going to look just like this. For positive x's, you take the absolute value of it.