Earlier, students explored some exponential functions with base \(e\) and learned about using the natural logarithm to find an unknown exponent in an equation with base \(e\). In this lesson, students integrate the two ideas. They 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).
- Use graphs to identify solutions to exponential equations.
- Use logarithms to calculate solutions to exponential equations.
- Let’s use graphs and logarithms to solve problems.
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.)
- I can solve exponential equations using logs or by graphing