Logarithmic Functions and Graphs

3.2 Logarithmic Functions and Their Graphs

Integrated Math 3

Mr. Washington

January 20, 2020

Objectives

• Recognize and evaluate logarithmic functions with base a.

• Graph logarithmic functions.

• Recognize, evaluate, and graph natural logarithmic functions.

•  Use logarithmic functions to model and solve real-life problems.

Evaluating Logarithms

Use the definition of logarithmic function to evaluate each logarithm at the indicated value of x.

Logarithmic Functions

The logarithmic function with base 10 is called the common logarithmic function. On most calculators, this function is denoted by the “log” key.

Evaluating Common Logarithms on a Calculator

Use a calculator to evaluate the function f (x) = log10 x at each value of x.

Using Properties of Logarithms

Solve for x

Multiple Choice

Simplify : $$\log_5\ 5^x$$   

• 5

• 1

• x

Multiple Choice

$$6^{\log_6\ 20}$$  

Simplify:

• 6

• x

• 20

Graphs of Logarithmic Functions 

To sketch the graph y = loga x, you can use the fact that the graphs of inverse functions are reflections of each other in the line y = x.

Graph of

 $y=\log_a\ x,\ a>1$  

Evaluating the Natural Logarithmic Function

Use a calculator to evaluate the function f (x) = ln x for each value of x.