Base e logarithm

Natural log

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.

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.

And log base e on your calculator is often written the natural log.

Round your answer to the nearest hundredth.

So we can rewrite this whole equation as the natural log of 1 plus v squared is equal to when you add natural logs, you can essentially just multiply the two numbers that you're taking the natural log of the natural log of, we could say, the absolute value of cx.

While natural log of y only includes numbers larger than 0.

I'm assuming it's maybe from french log naturelle or something like that.

And they called it the natural log because I'll show you e in a hundred different not a hundred, but in many different applications.

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

Well, you might ask, where did the 70 come from?

Let's get our calculator out and just calculate it.

little bit, an arbitrary constant c, we can really just write that as the natural log of the absolute value of some constant c.

And so the natural log of this is equal to the natural log of this.

And that's really not so special.

So what's the integral of 1 over y with respect to y?

I think you get the general idea here.

There's no need to see the little detailed words on it.

So ln of the absolute value of 1 plus 1 squared is equal to sine of 0 plus c.

And if you want, you can take the antiderivative of both sides with the natural logs, and all of that.

Or, in this case, the antiderivative of this is just the natural log of 1 plus v squared.

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

So natural log, that's this button over here ln .

Anyway, let me see if I can figure out what Excel's natural log function is.

You'll see other contexts where this would be described as natural.

And I'll show you, if you take this approach, what you get, OK?

The answer is that it's approximately 100 multiplied by the natural logarithm of two.

The natural and the supernatural.

And then, well, you would end up saying that the antiderivative is just the natural log of u.

Obviously this isn't drawn to scale.

So if this was a 1 over an x, or 1 over u, it's just the natural log of it.

I mean, this is still some arbitrary constant c.

It is divisible by 1, 2, 3 and 6.

So it's divisible by three natural numbers

So that would be 1, 2, 3, so on and so forth.

long distance travel, food processing.

You start taming that natural system.

Nature

Natural

So that's the antiderivative of 1 over y, and we proved that, or at least we proved that the derivative of natural

And this is just a slightly broader function, because it's domain includes positive and negative numbers, it just excludes 0.

So it only has 1 and itself.

So these are the whole numbers.

It's a whole number.