Education Technology

# Solving Logarithmic Equations

Math: Algebra II: Logarithms and Exponentials
9-12
45 Minutes
TI-Nspire™ CX
TI-Nspire™ CX CAS
TI-Nspire™ CX/CX II
TI-Nspire™ CX CAS/CX II CAS
4.5
Lessons
TNS

# Solving Logarithmic Equations

Activity Overview

Numeric, graphical and algebraic solutions to logarithmic equations.

Objectives

• Students will numerically approximate solutions to logarithmic equations
• Students will graphically determine exact solutions to logarithmic equations using the functions f(x) = loga(x) and f-1(x) = ax and the composition
• Students will find exact solutions to exponential equations using algebraic techniques that employ the relationship f ° f-1(x) = x

Vocabulary

• Exponential functions and equations
• Logarithmic functions and equations
• Inverse functions
• Composition of functions

This lesson involves numeric, graphical, and algebraic solutions to the equation log3(x) = 1.5. Students will:

• Analyze numeric patterns, predict an approximate solution, and evaluate predictions in a spreadsheet.
• Consider the graphs of both f(x) = log3(x) and f-1(x) =3x to determine that f(x) = 1.5 precisely when f-1(1.5) = x.
• Use the compositional relationship of logs(3x) = x to solve the equation. Since log3(31.5) = 1.5, the solution to the equation log3(x) = 1.5 is x = 31.5.
• Consider composition in the opposite order, solving the equation algebraically by employing 3log3(x) = x
• Use these techniques to solve similar equations.