In this lesson, students make a conjecture about logarithms in which the argument is raised to a power. First, students examine a pattern of logarithms in which the argument is raised to a power. In this lesson, the logarithms have integer values. Then, students write a conjecture about the pattern they notice and use the conjecture to evaluate logarithms that would be impossible for them to evaluate without the pattern. Finally, students prove their conjecture. They name the pattern the power rule, which states that a logarithm with an argument raised to a power is equivalent to the product of the power of the argument and the logarithm of the value without the power.

As students notice the pattern in logarithms they are making use of repeated reasoning (MP8) to generalize the pattern into a conjecture.