This lesson is optional because it goes beyond the depth of understanding required to address the standards. Students encounter real-world applications of logarithmic functions and use them to solve problems. They build log functions to represent the acidity of substances and the intensity of earthquakes. These applications give students opportunities to interpret key features of tables containing real-life data that can be modeled mathematically and to write functions to describe the relationships.

To describe and generalize the patterns in this lesson, students need to make use of structure (MP7). The quantitative relationships here may also be unfamiliar to students, so making sense of them requires persistence (MP1).

Students are not formally introduced to a logarithmic scale in this lesson.