# 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 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.)

### Student Facing

• I can interpret logarithmic functions in context.

### CCSS Standards

Building On

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.