Education Technology

Solving Logarithmic Equations

Published on 08/23/2011

Activity Overview

Numeric, graphical and algebraic solutions to logarithmic equations.


  • 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



  • 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 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.