CRP 762 Handout Logarithm
Source: http://www.sosmath.com/algebra/algebra.html (Section: Logarithms and Exponential
Definition of Exponential Function
xf(x)？aa is denoted by, where, and x is any real The exponential function f with base a，1
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).
Definition of Logarithmic Function
, we have >0 , and For x >0, aa，1
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 4？64
1；2？ The exponential equation 5can be written as the logarithmic equation ？25
？ Since logarithms are nothing more than exponents, you can use the rules of exponents
？ 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. On your
calculator, the base 10 logarithm is noted by log, and the base e logarithm is noted by ln.