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# Exponential Functions and Logarithms - Connecting the Dots

Lesson 8 of 21

## 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

#### Getting Started

*8 min*

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!

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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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- UNIT 1: Culture Building Unit - Welcome to the New Year!
- UNIT 2: Exponential and Logarithmic Functions
- UNIT 3: Sequences and Series
- UNIT 4: Statistics: Something for Everyone
- UNIT 5: Review Lessons
- UNIT 6: Writing Prompts in Mathematics
- UNIT 7: Trig Tidbits
- UNIT 8: Functions, Problem Solving, and 21st Century Skills
- UNIT 9: Polynomials and Problem Solving
- UNIT 10: Probability
- UNIT 11: Imagine This! Imaginary and Complex Numbers
- UNIT 12: Let's Explore Radicals!

- LESSON 1: Introduction to Exponential Functions - Rational Exponents
- LESSON 2: Real Number Exponents
- LESSON 3: A Conceptual Introduction to Exponential Functions: Collaboration, Questioning, and Financial Advice!
- LESSON 4: Discovering Solutions to Exponential Equations
- LESSON 5: An "Exponentially" Rewarding Battle!
- LESSON 6: Productive Struggle - A Pre-Spring Break Challenge of Exponential Functions
- LESSON 7: Compositions, Inverses & Role Play: Extending Concepts to Exponential Functions
- LESSON 8: Exponential Functions and Logarithms - Connecting the Dots
- LESSON 9: Exponentials and Logarithms: LOUD and CLEAR!
- LESSON 10: A Wrap on Logarithmic dB's and An Extension to Logarithmic Properties
- LESSON 11: Classroom Journey: Exponential and Logarithmic Properties
- LESSON 12: Laws of Logarithms and Real Applications
- LESSON 13: Calculator Boot-Camp and Solving Exponential Equations
- LESSON 14: Logs, Loans, and Life Lessons!
- LESSON 15: "Demystifying e" Day #1
- LESSON 16: Logs, Loans, and Life Lessons Collaboration Day!
- LESSON 17: FInal Discussion - "Demystifying e" PLUS Skills Practice with Logarithms
- LESSON 18: Elephant Tracks!
- LESSON 19: End of Unit Differentiated Problem Set
- LESSON 20: Differentiated Problem Share Out - Unit Review
- LESSON 21: Unit Review