Objectives

Students will state and apply the properties of logarithms:

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

Vocabulary

• Logarithmic expressions
• Equivalent expressions
• Exponential properties

About the Lesson

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.