Logarithmic function:

The inverse function of the exponential function is called the logarithmic function and is denoted as:  where is the base of the logarithm and

Properties of logarithmic functions:

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

Logarithms and how they relate to exponentials are 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 inverse functions is utilized to confirm that logarithms have inverses.

Examples of logarithms and their graphs are shown in the example problems. Logarithms are not defined at 0 compared to exponentials. Logarithms are solved using their properties 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 relationship between an exponential and a logarithm with the use of the inverse function principle.
• 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.

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