Education Technology

Solving Exponential Equations

Updated on 08/15/2014

Activity Overview

Numeric, graphical and algebraic solutions to an exponential equation.

Objectives

  • 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.

Vocabulary

  • 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.