- Topics At a Glance
**Linking Exponents and Logarithms**- Inverse Functions
- Rules for Inverse Functions
- The Base
**The Natural Log**- Exponential Functions
- Linear and Exponential Growth
- Exponential Growth and Decay
- Solving Exponential Equations
- Limits of Exponential Functions
- Logarithmic Functions
- Revisiting Inverse Operations
- Change of Base
- Limits of Logarithmic Functions
- Properties of Exponents and Logarithms
- In the Real World

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 *log _{e} x *or even

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

1. *x*^{3 }+ 7*x*

2. {-3,6; 0,0; 3,6; -1,-2}

3. *x*^{2} + 3*x* – 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.