# Solving Exponential Equations Using Logs

3 teachers like this lesson
Print Lesson

## 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.

## 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

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.

## Closure: Math Tweet

10 minutes

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.

## Homework

Assign worksheet #4 from this unit for homework tonight.