Exponential Functions and Logarithms - Connecting the Dots

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Objective

Students will be able to define logarithmic functions based on their knowledge of inverses and exponential functions. They will also establish strong connections between exponential and logarithmic functions

Big Idea

This lesson builds nicely on the studentsâ knowledge of inverse functions and introduces them to the world of logarithms. Rather than trying to memorize mathematical notation, the students are guided through an in-depth study under the umbrella of exponen

Lesson Author

Jarod Hammel

Huntington, IN

Grade Level

Eleventh grade

Subjects

Math

Algebra

Standards

HSF-IF.C.7e

Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

HSF-BF.B.5

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

HSF-LE.A.4

For exponential models, express as a logarithm the solution to ab<sup>ct</sup> = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology.

MP4

Model with mathematics.

MP7

Look for and make use of structure.

MP8

Look for and express regularity in repeated reasoning.

Getting Started

8 minutes

In this lesson, I begin class by handing back the previous day’s exit slip (or if you are doing this for the first time, hand out the exit slip as a “warm up”). While I take care of my start of class responsibilities I ask the students to compare exit slips and post any discrepancies to a www.polleverywhere.com poll that I have created. These polls are easy to create, clear from class to class and/or save as a PowerPoint slide… Plus they offer instant feedback from the students in a way that allows all students to be comfortable submitting.

Usually, once this is completed, we take time to look over the discrepancies and discuss what we are seeing. This leads us nicely into the lesson!

Lesson Middle

25 minutes

Addressing the Issue of Negatives

Work Time/ Additional Scaffolding + Homework

12 minutes

Rationale for the attached worksheet:

#1-5) Do the students know how logarithmic notation connects to exponential form?

#6-9) Can the students simplify a logarithm that can be written as an exponential equation? (These equations will all be able to be solved by finding like-bases, as in a previous lesson.)

#10-12) Can the students solve a logarithmic equation by converting it to exponential form? (Again, like bases will be the method for solving.)

#13-14) Extension questions that allow the students to “derive” their first laws of logarithms from their prior knowledge of exponential equations.

#15-16) Can the students mathematically reason and formulate arguments based on the concepts of the day? Can they extend these concepts to make a generalization about a special case?

#17-19) Can the students connect/contrast exponential functions to their logarithmic counterparts?

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