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The Natural Log

Another special type of logarithm you might see is the natural logarithm, usually written as ln(x) instead of log(x). Why the "n" comes after the "l" is a mystery to us, maybe it's log au naturel?

The natural log is the same as a regular log, except it has a base of e. e is an irrational number that represents the sum of and so on.

Weird, right? Sure, but it's really useful. You'll see it all the time in higher-level math, but we'll show you a common use in a later chapter.

Just to confuse you, some people will write ln x as loge x or even log x. We're not going to do that to you here. Keep an eye out, though!

Sample Problem

Are the following sets or functions one-to-one?

1. x3 + 7x
2. {-3,6; 0,0; 3,6; -1,-2}
3. x2 + 3x – 4
4. {1,3; 5,11; -1,-1}

Which of the following statements are true or false?

1. A one-to-one function must be even.
2. To be a function, an equation must be one-to-one.
3. To have an inverse, a function must be one-to-one.
4. An inverse of a function is the same as the reciprocal.

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