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# Applying Log Rules

Lesson 4 of 11

## Objective: SWBAT apply the properties of logarithms to condense or expand an expression.

## Big Idea: After students discover the properties of logs using slide rules they demonstrate their knowledge with a ticket out the door clicker quiz.

*50 minutes*

In the beginning part of today’s lesson, students will continue their work from yesterday on the NCTM lesson Logarithms Demystified-Student Worksheet - LogarithmsDemystified. You can access this original NCTM lesson here. Yesterday, students created their own logarithmic slide rules. I begin class by reviewing the use of the slider rulers: How to use the logarithmic rulers.

As students use these slide rules to explore rules for operations with logarithms, they will definitely be demonstrating **Mathematical Practice 5:** **using tools strategically **and **Mathematical Practice 8: ****Look for and express regularity in repeated reasoning.** Students will need to identify the patterns that are consistent when we are adding two logarithms or when we are subtracting two logarithms. Then, they will have to apply these patterns to solve the problems that go beyond their ruler scaling. This will also lead into **Mathematical Practice 7: seeing the structure in mathematics. **Students will need to identify the structure of a logarithm and how the properties enable problem solvers to leverage the structure. The students will encounter and discuss questions such as:

- What happens to the argument of a logarithm when we add two logarithms with the same base?
- What happens when we work with different bases?
- Does this rule seem familiar? How does it relate to exponent rules?

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Be sure that every student has correctly discovered the logarithm rules by reviewing answers as a class. Have students share their findings and make a class summary on the board so that there is a correct statement of the rules that can be shared. (Page 2 of the flipchart can also be displayed to summarize the properties of logarithms.)

After the discussion of the answers, students will need to apply the properties as they complete the clicker ticket out the door (pages 3-7 of flipchart). I require my students to complete these questions independently, so that I can get an accurate assessment of each students’ understandings at this time.

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- UNIT 1: Basic Functions and Equations
- UNIT 2: Polynomial Functions and Equations
- UNIT 3: Rational Functions and Equations
- UNIT 4: Exponential Functions and Equations
- UNIT 5: Logarithmic Functions and Equations
- UNIT 6: Conic Sections
- UNIT 7: Rotations and Cyclical Functions
- UNIT 8: Cyclical Patterns and Periodic Functions
- UNIT 9: Trigonometric Equations
- UNIT 10: Matrices
- UNIT 11: Review
- UNIT 12: Fundamentals of Trigonometry

- LESSON 1: What Is A Log?
- LESSON 2: Graphing and Shifting Logs
- LESSON 3: Discovering Log Rules (because logs rule!)
- LESSON 4: Applying Log Rules
- LESSON 5: Puzzling Log Equations
- LESSON 6: Solving Exponential Equations Using Logs
- LESSON 7: Experts on Exponential Equations
- LESSON 8: Modeling Exponentials Using Logarithms
- LESSON 9: Speed Dating with Logarithms
- LESSON 10: Logarithmic Equations Test Review
- LESSON 11: Logarithmic Equations Unit Test