In this activity, students will solve simple logarithmic equations and verify solutions using the corresponding exponential equations.

• exponential function
• domain
• one-to-one function
• logarithmic function
• range
• inverse function

This lesson involves the one-to-one function f(x) = b^x. In acknowledging the existence of its inverse, students will:

• Use the domain and range of f(x) to determine the domain and range of f^–1(x).
• Interpret the graph of f^–1(x) as the reflection of f(x) across the line y = x.
• Use this inverse relationship to write an equation for the graph of the inverse.
• Recognize the logarithmic notation needed to define the inverse function.
• Use the inputs and outputs of two inverse functions to complete a table and find patterns within the table.

As a result, students will:

• Solve simple logarithmic equations and verify solutions using the corresponding exponential equations.

*Note: This activity contains an optional AP Practice Questions document for those students preparing for the AP Precalculus Exam.