This lesson introduces students to logarithmic functions as functions of the form , where is a constant and is a positive number. In this unit, students focus on logarithms 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).
Learning Goals
Create graphs of logarithmic functions and use them to answer questions.
Describe (orally and in writing) characteristics of logarithmic functions.
A logarithmic function is a constant multiple of a logarithm to some base, so it is a function given by where is any number and is a positive number (10, 2, or 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.
Standards Alignment
Building On
HSA-SSE.A.1.a
Interpret parts of an expression, such as terms, factors, and coefficients.
For exponential models, express as a logarithm the solution to where , , and are numbers and the base is 2, 10, or ; evaluate the logarithm using technology.