- 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

Everyone has their limit; logs and exponents are no different.

Let's look at the exponential function *y* = 4*x*. No matter what value of *x* you throw into it, though, you can never get *y* to be negative or zero. (How optimistic of it.) Try a few:

4^{2}, 4^{3}, 4^{4} = 16, 64, 256

4^{0} = 1

4^{-2} = 1/4^{2} = 1/16

Using the following table, pick a *C* and *x* to fit an exponential function. Hint: remember that anything to the power of 0 becomes 1.

{2,18 ; 0,2 ; 3, 56}

Because any base raised to the power of 0 equals 1, we can easily figure out the coefficient. Throw that bad boy into the mix and solve:

*2 = C(b)^{0}*

2 = C(1)

C = 2

Now that you know *C*, use it to solve one of the other sets of variables given.

18 = 2(*b*)^{2}

9 = *b*^{2}*b *= 3

So the exponential function we need is *y* = 2(3^{x})