Logarithmic functions

The exponential function is a one-one function, with or .

This can also be noted:

The inverse of this function is the .

If

Let’s write

If we switch:

We note:

 

These equations are of the form:

Notation:

 is equivalent to

 

 Example:

Means

 

To solve:

We write:

 

The graph of the logarithmic function is the reflexion about y=x of the exponential function 

The domain is only the positive numbers with a a range of

The x-intercept is while there is no

It decreases if and it increases if

Properties of logarithms:

because

because

because

With

, with ,, and are positive real numbers and

Base change formula:

, with , , and are positive real numbers, , and

If:

, then

Here , , , and are positive real numbers, and