EXPONENTIAL FUNCTIONS
Definition of Exponential Function
The exponential function f with base a is denoted by , where , and x is any real number. The function value will be positive because a positive base raised to any power is positive. This means that the graph of the exponential function will be located in quadrants I and II.
For example, if the base is 2 and x = 4, the function value f(4) will equal 16. A corresponding point on the graph of would be (4, 16).
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.
If you are interested in reviewing any of the following topics, click the appropriate item:

 The properties of logarithms along with examples and problems, click on Properties

 The graphs of logarithms, with examples and problems, click on Graphs of Logarithms

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