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Lesson 3.2 Logarithmic Functions and Their Graphs...Lesson 3.2 Logarithmic Functions and Their...

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Tuesday, September 29,2009 Goals: Recognize and evaluate logrithmic functions with base a. Graph logrithmic functions with base a. Recognize, evaluate and graph natural logrithmic functions. Use logarithmic functions to model and solve reallife problems. Instructional DVD's: Logarithmic Functions and their Graphs. 34:47 DVD 2 Lesson 3.2 Logarithmic Functions and Their Graphs Title: Aug 19 9:03 PM (1 of 25)
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Page 1: Lesson 3.2 Logarithmic Functions and Their Graphs...Lesson 3.2 Logarithmic Functions and Their Graphs Title: Aug 19 9:03 PM (1 of 25) Definition of Logarithmic Function Title: Sep

Tuesday,  September 29, 2009

Goals: Recognize and evaluate logrithmic functions with base a.              Graph logrithmic functions with base a.              Recognize, evaluate and graph natural logrithmic functions.              Use logarithmic functions to model and solve real­life problems.Instructional DVD's: Logarithmic Functions and their Graphs. 34:47     DVD 2

Lesson 3.2Logarithmic Functions and Their Graphs

Title: Aug 19 ­ 9:03 PM (1 of 25)

Page 2: Lesson 3.2 Logarithmic Functions and Their Graphs...Lesson 3.2 Logarithmic Functions and Their Graphs Title: Aug 19 9:03 PM (1 of 25) Definition of Logarithmic Function Title: Sep

Definition of Logarithmic Function

Title: Sep 26 ­ 8:57 AM (2 of 25)

Page 3: Lesson 3.2 Logarithmic Functions and Their Graphs...Lesson 3.2 Logarithmic Functions and Their Graphs Title: Aug 19 9:03 PM (1 of 25) Definition of Logarithmic Function Title: Sep

Example 1 Evaluating Logarithms

Use the definition of logarithms to evaluate each logarithm at the indicatef value of x.

Title: Aug 24 ­ 5:28 PM (3 of 25)

Page 4: Lesson 3.2 Logarithmic Functions and Their Graphs...Lesson 3.2 Logarithmic Functions and Their Graphs Title: Aug 19 9:03 PM (1 of 25) Definition of Logarithmic Function Title: Sep

Example 2Evaluating Common Logs on a Calculator

Title: Aug 24 ­ 5:33 PM (4 of 25)

Page 5: Lesson 3.2 Logarithmic Functions and Their Graphs...Lesson 3.2 Logarithmic Functions and Their Graphs Title: Aug 19 9:03 PM (1 of 25) Definition of Logarithmic Function Title: Sep

Properties of Logarithms

Inverse Property

One­to­One Property

Title: Sep 26 ­ 8:58 AM (5 of 25)

Page 6: Lesson 3.2 Logarithmic Functions and Their Graphs...Lesson 3.2 Logarithmic Functions and Their Graphs Title: Aug 19 9:03 PM (1 of 25) Definition of Logarithmic Function Title: Sep

Example 3Using Properties of Logarithms

Title: Aug 24 ­ 5:39 PM (6 of 25)

Page 7: Lesson 3.2 Logarithmic Functions and Their Graphs...Lesson 3.2 Logarithmic Functions and Their Graphs Title: Aug 19 9:03 PM (1 of 25) Definition of Logarithmic Function Title: Sep

Graphs of Logarithmic Functions

Title: Aug 24 ­ 5:28 PM (7 of 25)

Page 8: Lesson 3.2 Logarithmic Functions and Their Graphs...Lesson 3.2 Logarithmic Functions and Their Graphs Title: Aug 19 9:03 PM (1 of 25) Definition of Logarithmic Function Title: Sep

Example 4Graphs of Exponential and Logarithmic Functions

Title: Aug 24 ­ 5:45 PM (8 of 25)

Page 9: Lesson 3.2 Logarithmic Functions and Their Graphs...Lesson 3.2 Logarithmic Functions and Their Graphs Title: Aug 19 9:03 PM (1 of 25) Definition of Logarithmic Function Title: Sep

Example 5

Sketching the Graph of Logarithmic Function 

Without calculator With calculator

1 2 3 4 5 6 7 8 9 10

1

­1

­2

2

3

Title: Aug 24 ­ 5:49 PM (9 of 25)

Page 10: Lesson 3.2 Logarithmic Functions and Their Graphs...Lesson 3.2 Logarithmic Functions and Their Graphs Title: Aug 19 9:03 PM (1 of 25) Definition of Logarithmic Function Title: Sep

Library of Parent Functions: Logarithmic Function 

Title: Sep 29 ­ 4:57 AM (10 of 25)

Page 11: Lesson 3.2 Logarithmic Functions and Their Graphs...Lesson 3.2 Logarithmic Functions and Their Graphs Title: Aug 19 9:03 PM (1 of 25) Definition of Logarithmic Function Title: Sep

Example 6Transformations of Graphs of Logarithmic Functions

Title: Aug 24 ­ 5:27 PM (11 of 25)

Page 12: Lesson 3.2 Logarithmic Functions and Their Graphs...Lesson 3.2 Logarithmic Functions and Their Graphs Title: Aug 19 9:03 PM (1 of 25) Definition of Logarithmic Function Title: Sep

The Natural Logarithmic Function

Title: Sep 29 ­ 5:02 AM (12 of 25)

Page 13: Lesson 3.2 Logarithmic Functions and Their Graphs...Lesson 3.2 Logarithmic Functions and Their Graphs Title: Aug 19 9:03 PM (1 of 25) Definition of Logarithmic Function Title: Sep

Example 7Evaluating the Natural Logarithmic Graph

Title: Aug 24 ­ 6:01 PM (13 of 25)

Page 14: Lesson 3.2 Logarithmic Functions and Their Graphs...Lesson 3.2 Logarithmic Functions and Their Graphs Title: Aug 19 9:03 PM (1 of 25) Definition of Logarithmic Function Title: Sep

Properties of Natural Logarithms

Inverse Property

One­to­One Property

Title: Sep 29 ­ 5:05 AM (14 of 25)

Page 15: Lesson 3.2 Logarithmic Functions and Their Graphs...Lesson 3.2 Logarithmic Functions and Their Graphs Title: Aug 19 9:03 PM (1 of 25) Definition of Logarithmic Function Title: Sep

Example 8 Using Properties of Natural Logarithms

Title: Aug 24 ­ 6:02 PM (15 of 25)

Page 16: Lesson 3.2 Logarithmic Functions and Their Graphs...Lesson 3.2 Logarithmic Functions and Their Graphs Title: Aug 19 9:03 PM (1 of 25) Definition of Logarithmic Function Title: Sep

Properties of Natural Logarithms

Title: Sep 26 ­ 10:12 AM (16 of 25)

Page 17: Lesson 3.2 Logarithmic Functions and Their Graphs...Lesson 3.2 Logarithmic Functions and Their Graphs Title: Aug 19 9:03 PM (1 of 25) Definition of Logarithmic Function Title: Sep

Example 9Finding the Domains of Logarithmic Functions

Find the domain of each function.

Title: Sep 26 ­ 10:04 AM (17 of 25)

Page 18: Lesson 3.2 Logarithmic Functions and Their Graphs...Lesson 3.2 Logarithmic Functions and Their Graphs Title: Aug 19 9:03 PM (1 of 25) Definition of Logarithmic Function Title: Sep

Example 10human memory model

Title: Sep 29 ­ 5:10 AM (18 of 25)

Page 19: Lesson 3.2 Logarithmic Functions and Their Graphs...Lesson 3.2 Logarithmic Functions and Their Graphs Title: Aug 19 9:03 PM (1 of 25) Definition of Logarithmic Function Title: Sep

Date: 

Classwork:  Computer:

  Homework:     

Lesson 3­2Page 203­204Problems  28, 32, 42, 50, 62, 66

Tuesday, September 29, 2009

Title: Aug 19 ­ 9:03 PM (19 of 25)

Page 20: Lesson 3.2 Logarithmic Functions and Their Graphs...Lesson 3.2 Logarithmic Functions and Their Graphs Title: Aug 19 9:03 PM (1 of 25) Definition of Logarithmic Function Title: Sep

Homework      page  _____   problem _______203 28

Title: Sep 25 ­ 4:49 AM (20 of 25)

Page 21: Lesson 3.2 Logarithmic Functions and Their Graphs...Lesson 3.2 Logarithmic Functions and Their Graphs Title: Aug 19 9:03 PM (1 of 25) Definition of Logarithmic Function Title: Sep

Homework      page  _____   problem _______203 32

Title: Sep 25 ­ 4:49 AM (21 of 25)

Page 22: Lesson 3.2 Logarithmic Functions and Their Graphs...Lesson 3.2 Logarithmic Functions and Their Graphs Title: Aug 19 9:03 PM (1 of 25) Definition of Logarithmic Function Title: Sep

Homework      page  _____   problem _______203 42

Title: Sep 25 ­ 4:49 AM (22 of 25)

Page 23: Lesson 3.2 Logarithmic Functions and Their Graphs...Lesson 3.2 Logarithmic Functions and Their Graphs Title: Aug 19 9:03 PM (1 of 25) Definition of Logarithmic Function Title: Sep

Homework      page  _____   problem _______204 50

Title: Sep 25 ­ 4:49 AM (23 of 25)

Page 24: Lesson 3.2 Logarithmic Functions and Their Graphs...Lesson 3.2 Logarithmic Functions and Their Graphs Title: Aug 19 9:03 PM (1 of 25) Definition of Logarithmic Function Title: Sep

Homework      page  _____   problem _______204 62

Title: Sep 25 ­ 4:49 AM (24 of 25)

Page 25: Lesson 3.2 Logarithmic Functions and Their Graphs...Lesson 3.2 Logarithmic Functions and Their Graphs Title: Aug 19 9:03 PM (1 of 25) Definition of Logarithmic Function Title: Sep

Homework      page  _____   problem _______204 62

Title: Sep 25 ­ 4:49 AM (25 of 25)


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