In this lesson, students use and prove the change of base rule for logarithms. First, students use their understanding of logarithms to recognize how logarithms and exponents can undo one another when the bases match. Then, students are introduced to the change of base rule, which allows logarithms to be rewritten into logarithms with other bases when this equation is used: . Students use this rule to calculate values for logarithms by changing them into logarithms in base 10 or base . Then they prove the change of base rule using the power rule for logarithms and the relationship they recognized in the Warm-up.

Students must make use of the structure (MP7) of logarithms to recognize their relationship to exponents and prove the change of base rule (MP7).