Solving Exponential Equations Using Logs

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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.

Lesson Author

Tiffany Dawdy

Phoenix, AZ

Grade Level

Twelfth grade

Subjects

Math

logarithms

Relations and Functions

logarithmic function

Standards

HSA-CED.A.1

Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.

HSF-BF.B.5

(+) Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.

MP1

Make sense of problems and persevere in solving them.

MP2

Reason abstractly and quantitatively.

MP3

Construct viable arguments and critique the reasoning of others.

MP6

Attend to precision.

MP7

Look for and make use of structure.

Warm-up: Homework Quiz

10 minutes

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.

Application: Solving Exponential Equations

10 minutes

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.

Check for Understanding: Clicker Questions

5 minutes

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.

Exploration: Change of Base Formula

15 minutes

How important is the Change of Base formula?

Solving Exponential Equations, Change of Base Reflection.MP4

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.