EXPONENTIAL AND LOGARITHMIC FUNCTIONS (Part-2)

─►Logarithmic Functions

Definition of Logarithmic Function
For x >0, a>0 , and , we have

Since x > 0, the graph of the above function will be in quadrants I and IV.

Comments on Logarithmic Functions

• The exponential equation could be written in terms of a logarithmic equation as .
• The exponential equation can be written as the logarithmic equation .
• Since logarithms are nothing more than exponents, you can use the rules of exponents with logarithms.
• Logarithmic functions are the inverse of exponential functions. For example if (4, 16) is a point on the graph of an exponential function, then (16, 4) would be the corresponding point on the graph of the inverse logarithmic function.
  
• The two most common logarithms are called common logarithms and natural logarithms. Common logarithms have a base of 10, and natural logarithms have a base of e. 

Graph of a Logarithmic Function (y = log _a x)