1. Chapter 10.3 Properties of Logarithms Standard & Honors
Algebra II Mr. Gilbert
Chapter 10.3
Properties of Logarithms
Standard & Honors
7/28/2019

2. Agenda Warm up Work book (participation grade) Lesson Homework
7/28/2019

3. Click the mouse button or press the Space Bar to display the answers.
7/28/2019
Click the mouse button or press the Space Bar to display the answers.
Transparency 3

4. 7/28/2019
Transparency 3a

5. Homework Review
7/28/2019

6. Communicate Effectively
Richter Scale – earthquakes
Decibel Scale – sound
Magnitude of light from stars
Recall the properties of exponents:
(an)(am)=an+m for example (34)(35)=3(4+5)=39
(an)/(am)=an-m for example (53)(52)=5(3-2)=5
7/28/2019

7. Example 1 Use the Product Property (2)
Example 2 Use the Quotient Property (2)
Example 3 Use Properties of Logarithms (4)
Example 4 Power Property of Logarithms (2)
Example 5 Solve Equations Using Properties of Logarithms (6)
7/28/2019
Lesson 3 Contents

8. Use to approximate the value of
Replace 250 with 53 • 2.
Product Property
Inverse Property of Exponents and Logarithms
Replace with
Answer: Thus, is approximately
7/28/2019
Example 3-1a

9. Use to approximate the value of
Answer:
7/28/2019
Example 3-1b

10. Use and to approximate the value of
Replace 4 with the
quotient
Quotient Property
and
Answer: Thus is approximately
7/28/2019
Example 3-2a

11. Use and to approximate the value of
Answer:
7/28/2019
Example 3-2b

12. Let L1 be the loudness of one lawnmower running.
Sound The loudness L of a sound in decibels is given by where R is the sound’s relative intensity. The sound made by a lawnmower has a relative intensity of 109 or 90 decibels. Would the sound of ten lawnmowers running at that same intensity be ten times as loud or 900 decibels? Explain your reasoning.
Let L1 be the loudness of one lawnmower running.
Let L2 be the loudness of ten lawnmowers running.
7/28/2019
Example 3-3a

13. Then the increase in loudness is L2 – L1.
Substitute for L1 and L2.
Product Property
Distributive Property
Subtract.
Inverse Property of Exponents and Logarithms
7/28/2019
Example 3-3b

14. Answer:. No; the sound of ten lawnmowers is perceived
Answer: No; the sound of ten lawnmowers is perceived to be only 10 decibels as loud as the sound of one lawnmower, or 100 decibels.
7/28/2019
Example 3-3c

15. Sound The loudness L of a sound in decibels is given by
Sound The loudness L of a sound in decibels is given by where R is the sound’s relative intensity. The sound made by fireworks has a relative intensity of 1014 or 140 decibels. Would the sound of ten fireworks of that same intensity be ten times as loud or 1400 decibels? Explain your reasoning.
Answer: No; the sound of ten fireworks is perceived to be only 10 more decibels as loud as the sound of one firework, or 150 decibels.
7/28/2019
Example 3-3d

16. Given that approximate the value of
Replace 216 with 63.
Power Property
Replace with
Answer:
7/28/2019
Example 3-4a

17. Given that approximate the value of
Answer:
7/28/2019
Example 3-4b

18. Property of Equality for Logarithmic Functions
Solve .
Original equation
Power Property
Quotient Property
Property of Equality for Logarithmic Functions
Multiply each side by 5.
7/28/2019
Example 3-5a

19. Take the 4th root of each side.
Answer:
Take the 4th root of each side.
7/28/2019
Example 3-5b

20. Definition of logarithm
Solve .
Original equation
Product Property
Definition of logarithm
Subtract 64 from each side.
Factor.
Zero Product Property or
Solve each equation.
7/28/2019
Example 3-5c

21. Check Substitute each value into the original equation.
Replace x with –4.
Since log8 (–4) and log8 (–16) are undefined, –4 is an extraneous solution and must be eliminated.
Replace x with 16.
Product Property
7/28/2019
Example 3-5d

22. Definition of logarithm
Answer: The only solution is
7/28/2019
Example 3-5d

23. Solve each equation. a. b.
Answer: 12
Answer: 8
7/28/2019
Example 3-5e

24. Homework - Honors See Syllabus 10.3 pp. 544 – 545: 21 – 33 odd
7/28/2019

25. Homework
See Syllabus 10.3
pp. 544 – 545: 21 – 33 odd
7/28/2019