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# Solving Exponential Equations Using Logs

Lesson 6 of 11

## Objective: SWBAT solve exponential equations and explain the change of base formula for logarithms.

## Big Idea: Learning to use logs to solve exponential equations leads into discovery of the change of base formula which is summarized in a Math Tweet.

*50 minutes*

#### Warm-up: Homework Quiz

*10 min*

Students will spend the first 10 minutes of class today preparing for and taking their weekly Homework Quiz* *over worksheets #1-3 from the logarithms unit. As they complete their homework quizzes, students should transition to the next section of the class and start working on the Solving Exponential equations worksheet.

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I will first direct students to complete questions 1-5 on their Student Worksheet in their teams. The worksheet demonstrates how to solve an exponential equation by taking the log of both sides. I will encourage students to work with their team and discuss/compare their answers. Students should have access to a graphing calculator while completing this worksheet. While students are working on this I will be displaying page 2 of the flipchart. As students finish up that section they should copy this page of notes down.

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After about 10 minutes have passed and/or most of the class is progressing onto the back page of the worksheet, I ask students to answer some clicker questions. The questions are from pages 3-5 of the flipchart - solving exponential equations and change of base. This brief activity provides a quick check for understanding. This check-in will help me to assess whether or not students can solve a basic exponential equations using logs. At the same time, it provides an opportunity for students to take an initial step toward multi-step exponential equations.

Once students text in their answers, I plan to model the solution method for students who answer incorrectly.

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After the check-in (and demonstration) students will work through questions 6-8 on page 2 of the Worksheet. Here, they will use their knowledge of the **Power Law of Logarithms** to solve exponential equations. I hope that students will catch on to what is happening and take a big step towards understanding the **Change of Base Formula**. They will also learn how to graph logarithmic functions on their calculator.

At the conclusion of this section, I will present page 6 of the flipchart to formalize the change of base formula for students.

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#### Closure: Math Tweet

*10 min*

Present page 7 of the flipchart and have students do a **Math Tweet **by texting a ‘tweet’ sized explanation of the change of base formula.

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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