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 .

Exponential functions have inverses which are the logarithms functions that are described in this tutorial. The domain of logarithms is only defined for values greater than zero. The concept of one to one functions is used to verify that logarithms have inverses.

Examples of logarithms are graphically shown in a section of this tutorial. Properties of logarithms are similar to the ones of exponentials because one is an inverse of another. Logarithms properties are used to solve expressions. Application of logarithms in economics and finance are used in word problems.

Specific Tutorial Features:
• Examples to illustrate logarithms and their properties.
• 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