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Algebra 2: What is Log?
by Texas Instruments

#### Objectives

• 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

#### Vocabulary

• 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.