I know your gut reaction is the natural log of y, which is correct, but there's actually a slightly broader function than that, whose derivative is actually 1 over y, and that's the natural log of the absolute value of y.

So let's say that we wanted to compare the absolute value of 2 to the absolute value of 3.

But the easy way to calculate absolute value signs, if you don't care too much about the concept is whether it's negative or positive, the absolute value of it is always going to be positive.

Now, you could integrate both sides of this, and you'll get the natural log of the absolute value of x is equal to the natural log of the absolute value of mu, et cetera, et cetera.

So in general absolute value will always be a positive quantity.

I'm definitely not going back home!

But anyway, that's the left hand side, and then that equals Well, this one's easy.

Because here, that obviously works for positive values, because the absolute value of x will be equal to x.

If it's a positive number already, it just equals itself, when you take the absolute value.

But if you had some negative numbers here, you would actually say the absolute value of numerator is lesser than the absolute value of the denominator, for a proper fraction

Leave you again

I finally met

Yeah, superspecial sure.

In the magenta situation, the thing in the absolute value sign was positive 2, because this was a situation where we assumed that the thing in the absolute value sign was a positive 2.

You are never going to feel like it.

Okay?

Now, this should cause you some pause, because when you take the absolute value of anything, what do you know you're going to get?

Never Ever Ever!

But if you think about it in kind of just very simple terms, if it's a negative number, it becomes a positive version of it.

love for someone

Do, 'cause we should definitely...

We can do it.

We can make this work.

Absolutely!

You haven't thought about that?

Definitely!

Definitely.

Never!

Never!

Obviously. No.

Ever?

So both of these things evaluate to 8.

I'll do it in orange, the absolute value of negative 3, we just figured out, that is positive 3.

Definitely.

Whatever you do, don't fall asleep.

But you can't visit him!

And we're left with v is equal to the natural log of the absolute value of x plus c.

Looks like I got you by the balls, Abby.

absolute

You have carte blanche.

I'm sure of it.

Then, as to money? You have carte blanche.

You're smart because you have something to offer.

I should have had more faith in his pure, fine spirit.

Does this luxurious flat belong to my nephew Francis?