Section 4.4 Logarithmic Functions. Definition:Definition: 2) A logarithm is merely a name for a certain exponent! 2) A logarithm is merely a name for.

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Presentation transcript:

Section 4.4 Logarithmic Functions

Definition:Definition: 2) A logarithm is merely a name for a certain exponent! 2) A logarithm is merely a name for a certain exponent! Important Result… 1) The log function and the exponential functions are inverses of each other! Important Result… 1) The log function and the exponential functions are inverses of each other!

1. Special Logarithms - base 10 and e

2. Changing from log to exponential form

3. Changing from exponential to log form

4. Evaluating Logarithms

5. Special Properties

Inverse Functions Switch and solve: 1)Replace f(x) with y: 2)Interchange x and y: 3)Solve for y: 4)Replace y with Switch and solve: 1)Replace f(x) with y: 2)Interchange x and y: 3)Solve for y: 4)Replace y with 6. Log is the Inverse of Inverse Property of Logarithms

Sketch the inverse of reflecting graph of over Sketch the inverse of reflecting graph of over Domain: Range: Key Points: Asymptotes: 7.Graphing the inverse of

Graph directly a)Key Points b)Domain c)Range d)Asymptotes

a)Key Points b)Domain c)Range d)Asymptotes

8 Two Methods for Graphing Log Functions Method 1: Directly Method 2: Use Inverse

a)Key Points of parent b) Transformations c) Domain d)Range e) Asymptotes Method 1: Determine the graph of a log function, using transformations of the parent function.

1) Find 2)Graph 3)Reflect over y = x to graph Method 2: Determine the graph of a log function by graphing its inverse function and reflect over y=x

9. Domain of a logarithmic function Determine the domain for these functions.

10. Change-of-Base Formula Example. Find an approximation for

Log = Constant 11. Solving: Log = Constant Logarithmic Equations Solve for variable inside the log expression. Logarithmic Equations Solve for variable inside the log expression. Use the definition: Use the definition:

Exponential = Constant 12. Solving: Exponential = Constant Solve for variable in the exponent Use the definition: Use the definition:

11. Log = Log 11. Solving: Log = Log If then M = N Solve for variable inside log on each side. When solving log functions, we must check that a solution lies in the domain!

Summary: Inverse Properties of Logarithmic and Exponential Functions The Logarithmic and Exponential Functions are inverses of each other. The Logarithmic and Exponential Functions are inverses of each other. Example of the relationship: Let Inverse Property of

Exponential functions and log functions are inverse functions of each other. Domain: Range: Key Points: Asymptotes: Graphing Logarithmic Functions