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Definition of Exponential Function

By Sue Perkins,2014-11-26 11:38
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Definition of Exponential Function

CRP 762 Handout Logarithm

    Source: http://www.sosmath.com/algebra/algebra.html (Section: Logarithms and Exponential

    Functions)

    Definition of Exponential Function

    xf(x)aa is denoted by, where, and x is any real The exponential function f with base a1

    number. The function value will be positive because a positive base raised to any power is

    xf(x)apositive. 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

    xf(x)2point on the graph of would be (4, 16).

     1

Definition of Logarithmic Function

    , we have >0 , and For x >0, aa1

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

Comments on Logarithmic Functions

    3 The exponential equation could be written in terms of a logarithmic equation as 464

    log(64)3. 4

    12 The exponential equation 5can be written as the logarithmic equation 25

    1log()2. 525

     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.

     2

     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. On your

    calculator, the base 10 logarithm is noted by log, and the base e logarithm is noted by ln.