A naive definition of exponentiation would be:

But what happens when b is not a natural number?

Then, a better definition is:

where "exp" is:

where "ln" (the "natural logarithm") is:

## Properties of "exp"

- exp(x, x positive) rises very very quickly.

## Other Logarithms

where:

## Properties of (all) Logarithms

- (for positive x,y)
- (for positive x,y)