- Students will numerically approximate the solution to exponential equations
- Students will graphically determine exact solutions to exponential equations using the functions f(x) = ax and f-1(x) = loga(x) and the composition f ° f-1(x) = x
- Students will find the exact solution to exponential equations using algebraic techniques that employ the relationship.
- Exponential functions and equations
- Logarithmic functions and equations
- Inverse functions
- Composition of functions
About the Lesson
This lesson involves numeric, graphical, and algebraic solutions to the equation 2x = 3. As a result, students will:
- Analyze numeric patterns to predict an approximate solution in a spreadsheet.
- Consider the graphs of both f(x) = 2x and f-1(x) = log2(x) to determine that f(x) = 3 precisely when f-1(3) = x.
- Use the compositional relationship of 2log2(x) = x to solve the equation. That is, the solution to the equation 2x = 3 is x = log23, since 2log2(3) = 3.
- Consider composition in the opposite order. That is, they will employ the fact that log2(2x) = x to solve the equation algebraically.
- Use these techniques to solve similar equations.