In this lesson, students use the natural logarithm and representations of exponential functions to solve problems in context.

Students see that graphs representing exponential functions can be used to estimate logarithms. They also see that logarithms enable them to solve exponential equations and answer questions about exponential functions without graphing.

As students make sense of the connections between the parameters in equations, the features of graphs, and the descriptions of functions, they practice reasoning concretely and abstractly (MP2). When they explain how to use exponential graphs to estimate logarithms and defend why certain logarithms do or don’t represent solutions to exponential equations, students practice constructing reasoned arguments (MP3) and attending carefully to the meanings of expressions and equations (MP6).