Exponential and Logarithmic Functions 3 Exponential and Logarithmic Functions Copyright © Cengage Learning. All rights reserved.

Logarithmic Function and Their Graphs 3.2 Copyright © Cengage Learning. All rights reserved.

Graphs of Logarithmic Functions

Graphs of Logarithmic Function  

Example 4 – Graph of Exponential and Logarithmic Function In the same coordinate plane, sketch the graph of each function by hand. a. f (x) = 2x b. g (x) = log2x Solution: Use the points from the previous slide to plot points and connect graph with a smooth curve.

Example 4 – Solution cont’d The graph of g (x) = log2x is a reflection of the graph of f (x) = 2x in the line y = x, as shown in the graph on the previous page. This is due to the fact that the graphs of inverse functions are always reflections of each other in the line y = x.

Logarithmic Functions

Logarithmic Function

Logarithmic Function Every logarithmic equation can be written in an equivalent exponential form and every exponential equation can be written in logarithmic form. The equations y = logax and x = ay are equivalent. When we say or use a logarithm, it is because we are looking for the unknown exponent.

Example 1 – Evaluating Logarithms Use the definition of logarithmic function to evaluate each logarithm at the indicated value of x. (Remember that logarithm means you are looking for an exponent.) Function Value a. f (x) = log2x x = 32 b. f (x) = log3x x = 1 c. f (x) = log4x x = 2 d. f (x) = log10x x =

Example 1 – Solution a. f (32) = log232 = 5 because 25 = 32. b. f (1) = log31 = 0 because 30 = 1. c. f (2) = log42 = because 34/2 = = 2. d. f ( ) = log10 = – 2 because 10–2 = = .

Logarithmic Function The logarithmic function with base 10 is called the common logarithmic function. The following properties follow directly from the definition of the logarithmic function with base a.