Lesson 17: Logarithmic Functions
About this lesson
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 Warmup: 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 Cooldown: 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.)
Glossary:
 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.
Standards:
 This lesson builds on the standard: CCSS.HSASSE.A.1.aMS.ASSE.1aMO.A1.SSE.A.1
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