Definitions

We define the natural logarithm to be the inverse of e^x:

ln(x) = (e^x)^-1 implies ln(e^x) = x

Graph

Properties

1. ln(1) = 0, ln(e) = 1

2. ln(uv) = ln(u) + ln(v)

3. ln(u^v) =vln(u)

4.

Proof of 2

Proof of 3

Proof of 4

Derivative

Proof