Education Technology

Mathematics lessons for IB® Diploma Programme

Applications and Interpretation | Numbers and Algebra

Properties of Logs

Activity Overview

This lesson is based on observing counter-examples to logarithmic rules and involves comparing the values of several base 2 logarithmic expressions to discover which produce the same result. As a result, students will:

  • Generalize these rules for base a, where a is a real number, a > 0 and a ≠ 1.
  • Compare these logarithmic properties to their exponential counterparts.


Students will state and apply the properties of logarithms:

  • loga(m*n) = loga(m) + loga(n)
  • loga(m/n) = loga(m) - loga(n)
  • loga(mn) = n*loga(m)


  • Logarithmic expressions
  • Equivalent expressions
  • Exponential properties