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

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

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Homework Review 7/28/2019

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

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

Use to approximate the value of Replace 250 with 53 • 2. Product Property Inverse Property of Exponents and Logarithms Replace with 0.4307. Answer: Thus, is approximately 3.4307. 7/28/2019 Example 3-1a

Use to approximate the value of Answer: 6.5850 7/28/2019 Example 3-1b

Use and to approximate the value of Replace 4 with the quotient Quotient Property and Answer: Thus is approximately 0.7737. 7/28/2019 Example 3-2a

Use and to approximate the value of Answer: 1.2920 7/28/2019 Example 3-2b

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

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

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

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

Given that approximate the value of Replace 216 with 63. Power Property Replace with 1.1133. Answer: 7/28/2019 Example 3-4a

Given that approximate the value of Answer: 5.1700 7/28/2019 Example 3-4b

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

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

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

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

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

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

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

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