# Activities

• • • ##### Subject Area

• Math: Algebra II: Logarithms and Exponentials

• ##### Author 9-12

45 Minutes

• ##### Device
• TI-Nspire™
• TI-Nspire™ CAS
• TI-Nspire™ CX/CX II
• TI-Nspire™ CX CAS/CX II CAS
• TI-Nspire™ Navigator™
• TI-Nspire™ Apps for iPad®
• ##### Software

TI-Nspire™
TI-Nspire™ CAS

3.6

## Solving Exponential Equations

#### 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.