Solve simple logarithmic equations and verify solutions using the corresponding exponential equations.
- Students will recognize the function g(x) = logx(x) as the inverse of f(x)=bx where b > 0 and b ≠ 1
- Students will apply this inverse relationship and solve simple logarithmic equations
- Exponential function
- Logarithmic function
- One-to-one function
- Inverse function
- Domain and range
About the Lesson
This lesson involves the one-to-one function f(x)=bx. 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.
As a result, students will:
- Solve simple logarithmic equations and verify solutions using the corresponding exponential equations.