Course: Intermediate Algebra
Topic: Exponential and Logarithmic Functions
Subtopic: Logarithmic Functions & Graphs


After studying exponential functions, it seems a natural question to ask, what is the inverse of an exponential function? What function "undoes" say 2x enabling you to solve for x in the equation 2x=5 for instance? Well, a logarithmic function is the inverse of an exponential function. Logarithms such as log3x (read "log base 3 of x") have their own graphs and algebraic rules. These special functions are the focus of this lesson.

The conversion from exponential to logarithmic form (and visa versa) is particularly important to learn. Try to keep in mind that 23=8 and log28=3 say the same thing just in different forms (exponential form and logarithmic form, respectively).

As you study these new functions be sure to examine them both algebraically and graphically. Recognize connections between logarithmic and exponential functions and the differences between a common logarithm (log(x)) and a natural logarithm (ln(x)).


By the end of this topic you should know and be prepared to be tested on:


Terms you should be able to define: base of logarithm, input to logarithm, output from logarithm, notation associated with writing logarithms, common logarithm, natural logarithm, logarithmic function, vertical asymptote line