Chapter 10.2 Logarithms and Logarithmic Functions Standard & Honors

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Presentation transcript:

Chapter 10.2 Logarithms and Logarithmic Functions Standard & Honors Algebra II Mr. Gilbert Chapter 10.2 Logarithms and Logarithmic Functions Standard & Honors 11/27/2018

Agenda Warm up Decay project Lesson Homework 11/27/2018

Homework Review 11/27/2018

Communicate Effectively Logarithm: the inverse of the exponential function y=bx is x=by and it is called the logarithm of x. Logarithm of x: is usually written y=logb x Logarithmic function: y=logb x, where b>0 and b1. Common Usage Sound scale: decibels Earthquake scale: Richter scale. 11/27/2018

Example 1 Logarithmic to Exponential Form (2) Example 2 Exponential to Logarithmic Form (2) Example 3 Evaluate Logarithmic Expressions (2) Example 4 Inverse Property of Exponents and Logarithms (2) Example 5 Solve a Logarithmic Equation (2) Example 6 Solve a Logarithmic Inequality (3) Example 7 Solve Equations with Logarithms on Each Side (3) Example 8 Solve Inequalities with Logarithms on Each Side (2) 11/27/2018 Lesson 2 Contents

Write in exponential form. Answer: Write in exponential form. Answer: 11/27/2018 Example 2-1a

Write each equation in exponential form. a. b. Answer: Answer: 11/27/2018 Example 2-1c

Special Values If b>0 and b1 then the following is true: 11/27/2018

Special Equalities Because and are inverses: 11/27/2018

Write in logarithmic form. Answer: Write in logarithmic form. Answer: 11/27/2018 Example 2-2a

Write each equation in logarithmic form. a. b. Answer: Answer: 11/27/2018 Example 2-2c

Let the logarithm equal y. Evaluate Let the logarithm equal y. Definition of logarithm Property of Equality for Exponential Functions Answer: So, 11/27/2018 Example 2-3a

Evaluate Answer: 3 11/27/2018 Example 2-3b

Evaluate . Answer: Evaluate . Answer: 11/27/2018 Example 2-4a

Evaluate each expression. a. b. Answer: 3 Answer: 11/27/2018 Example 2-4c

Definition of logarithm Solve Original equation Definition of logarithm Power of a Power Simplify. Answer: 11/27/2018 Example 2-5a

Solve Answer: 9 11/27/2018 Example 2-5b

Solve Check your solution. Original inequality Logarithmic to exponential inequality Simplify. Answer: The solution set is 11/27/2018 Example 2-6a

Check Try 64 to see if it satisfies the inequality. Original inequality Substitute 64 for x. 11/27/2018 Example 2-6b

Solve Check your solution. Answer: 11/27/2018 Example 2-6c

Solve Check your solution. Original equation Property of Equality for Logarithmic Functions Subtract 4x and add 3 to each side. Factor. Zero Product Property or Solve each equation. 11/27/2018 Example 2-7a

Check Substitute each value into the original equation. Substitute 3 for x. Simplify. Original equation Substitute 1 for x. Simplify. Answer: The solutions are 3 and 1. 11/27/2018 Example 2-7b

Solve Check your solution. Answer: The solutions are 3 and –2. 11/27/2018 Example 2-7c

Property of Inequality for Logarithmic Functions Solve Original inequality Property of Inequality for Logarithmic Functions Addition and Subtraction Properties of Inequalities We must exclude all values of x such that or Thus the solution set is and This compound inequality simplifies to Answer: The solution set is 11/27/2018 Example 2-8a

Solve Answer: 11/27/2018 Example 2-8b

Homework - Honors See Syllabus 10.2 pp. 536-537: 21-63 (multiples of 3), 68-72 11/27/2018

Homework See Syllabus 10.2 pp. 536-537: 21-32, 39-44, 47-59 (multiples of 3), 68-70 11/27/2018