Logarithmic function:

The inverse function of the exponential function is called the logarithmic function and is denoted as:  where a is the base of the logarithm and it is must be >0 and not equal to one.

Properties of logarithmic functions:

1) If and then .
2) If then .
3) If then .
4) If then .
5) If and  then .

Logarithms are the inverse functions of exponentials as it is described in this tutorial.  The graphs of logarithms follow the same rules as the ones of exponentials except they are not defined at zero. The concept of one to one functions is used to verify that logarithms have inverses.

Examples of logarithms are shown with the use of graphs. Properties of logarithms are similar to the ones of exponentials except that they are not defined at zero. Logarithms properties are used to solve expressions involving them and are presented in the examples.

Specific Tutorial Features:

• Examples to illustrate the properties and applications of logarithms.
• Animated diagrams to actually show the inverse relationship between an exponential and a logarithm.
• Problem-solving techniques are used to work out and illustrate the example problems, step by step.

Series Features:

• Concept map showing inter-connections of new concepts in this tutorial and those previously introduced.
• Definition slides introduce terms as they are needed.
• Visual representation of concepts
• Animated examples—worked out step by step
• A concise summary is given at the conclusion of the tutorial.

Preliminaries of logarithms
Logarithms functions and their properties
	        Definition of logarithms
	        Properties of logarithms
           Logarithmic equations
Common and Natural Logarithms
           Euler Number 
           Logarithms with different bases
	        Application of logarithms