Lesson 17

Logarithmic Functions

Lesson Narrative

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.

Learning Goals

Teacher Facing

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

Student Facing

  • Let’s graph log functions.

Required Materials

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.)

Learning Targets

Student Facing

  • I can interpret logarithmic functions in context.

CCSS Standards

Glossary Entries

  • 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.