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Logarithms and Exponential Functions

Logarithms and Exponential Functions

 Table of Contents

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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