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Lesson plan

Lesson 17: Logarithmic Functions

teaches Common Core State Standards MP5 http://corestandards.org/Math/Practice/MP5
teaches Common Core State Standards MP6 http://corestandards.org/Math/Practice/MP6
teaches Common Core State Standards MP7 http://corestandards.org/Math/Practice/MP7
teaches Common Core State Standards MP2 http://corestandards.org/Math/Practice/MP2
teaches Common Core State Standards HSF-LE.A.4 http://corestandards.org/Math/Content/HSF/LE/A/4
teaches Common Core State Standards HSF-IF.C http://www.corestandards.org/the-standards
teaches Common Core State Standards HSF-IF.C.7.e http://corestandards.org/Math/Content/HSF/IF/C/7/e

Lesson 17: Logarithmic Functions

This lesson introduces students to logarithmic functions in base 2 and base 10. Building from the work students have done in the previous lessons with logarithms from an exponential point of view, students make sense of logarithmic functions in a familiar context of population growth. They interpret the equations that represent the functions, graph the functions, and consider why the graphs representing logarithmic functions behave a certain way (MP2, MP7).

Students will continue their study of logarithmic functions in a future course, so this lesson is intended as an introduction to them and is closely tied to their work with exponential functions.

Lesson overview

  • 17.1 Warm-up: Which One Doesn’t Belong: Functions (5 minutes)
  • 17.2 Activity: How Long Will It Take? (20 minutes)
  • 17.3 Activity: Another Logarithmic Function (10 minutes)
    • Includes "Are you Ready for More?" extension problem
  • Lesson Synthesis
  • 17.4 Cool-down: Which Graph Represents Which Function? (5 minutes) 

Learning goals:

  • Create graphs of logarithmic functions and use them to answer questions.
  • Describe (orally and in writing) characteristics of logarithmic functions.

Learning goals (student facing):

  • Let’s graph log functions.

Learning targets (student facing):

  • I can interpret logarithmic functions in context.

Required materials:

  • Graphing technology

Required preparation:

  • Acquire devices that can run Desmos (recommended) or other graphing technology.
  • It is ideal if each student has their own device. (Desmos is available under Math Tools.)


  • logarithmic function - A logarithmic function is a constant multiple of a logarithm to some base, so it is a function given by \(f(x) = k \log_{a}(x)\) where \(k\) is any number and \(a\) is a positive number (10, 2, or \(e\) in this course). The graph of a typical logarithmic function is shown. Although the function grows very slowly, the graph does not have a horizontal asymptote.

  • Access the complete Algebra 2 Course glossary. 


  • This lesson builds on the standard: CCSS.HSA-SSE.A.1.aMS.A-SSE.1aMO.A1.SSE.A.1






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