EXPONENTIAL FUNCTIONS

Definition of Exponential Function

The exponential function f with base a is denoted by tex2html_wrap_inline38 , where tex2html_wrap_inline40 , 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 tex2html_wrap_inline38 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 tex2html_wrap_inline46 would be (4, 16).

Definition of Logarithmic Function

For x >0, a>0 , and tex2html_wrap_inline40 , we have

displaymath54

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

Comments on Logarithmic Functions

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
  • Change of base with respect to logarithms with examples and problems, click on Change of base
  • The three rules of logarithms, with examples and problems, click on Rules of Logarithms
  • Solving exponential and logarithms equations with examples and problems, click on Solving Equations
  • Solving word problems involving exponential and logarithms functions with examples and problems, click on Solving Word Problems

  • [Exponential Rules] [Logarithms]

    [Algebra] [Trigonometry ] [Complex Variables]

    S.O.S MATHematics home page

    Do you need more help? Please post your question on our S.O.S. Mathematics CyberBoard.

    Author: Nancy Marcus

    Copyright 1999-2016 MathMedics, LLC. All rights reserved.
    Contact us
    Math Medics, LLC. - P.O. Box 12395 - El Paso TX 79913 - USA
    users online during the last hour