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Logarithmic Functions. Dr. Johnny Duke Georgia Highlands College. Inverse. In mathematics we like to be able to “undo” whatever has been done. - PowerPoint PPT Presentation
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Logarithmic Logarithmic FunctionsFunctions
Dr. Johnny DukeGeorgia Highlands College
InverseInverse
In mathematics we like to be able to “undo” whatever has been done.
For instance, a child learns to add, then learns to subtract which “undoes” addition. Once one learns to multiply, then division is learned to “undo” multiplication.
These are inverse operations.
Inverse FunctionsInverse Functions
The Inverse of Exponential The Inverse of Exponential
FunctionsFunctions
PracticePractice
Definition AppliedDefinition Applied
PracticePractice
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Graphs of Graphs of Logarithmic Logarithmic FunctionsFunctions
Dr. Johnny Duke
• ..\gsp\log base 2.gsp
Transformations and Logarithmic Transformations and Logarithmic
FunctionFunction
Horizontal Shift, left one unit.
Transformations and Logarithmic Transformations and Logarithmic
FunctionFunction
Vertical Shift, up two units.
Transformations and Logarithmic Transformations and Logarithmic
FunctionFunction
Reflection throughx-axis
Transformations and Logarithmic Transformations and Logarithmic
FunctionFunction
Reflection throughy-axis
Transformations and Logarithmic Transformations and Logarithmic
FunctionFunction
Reflection throughx-axis; vertical shift down 4 units; horizontal shift right 2 units.
•Stop
Two Special Logarithmic Two Special Logarithmic
FunctionsFunctions
Two Special Logarithmic Two Special Logarithmic
FunctionsFunctions
PracticePractice
1
1.398
1.792
-2
e
- .981
Change of Base FormulaChange of Base Formula
PracticePractice
stopstop
Properties of Properties of Logarithmic Logarithmic FunctionsFunctions
Dr. Johnny Duke
Properties of logarithmic functionsProperties of logarithmic functions
Properties of logarithmic Properties of logarithmic
functionsfunctions
More Properties of LogsMore Properties of Logs
Expanding logarithmic Expanding logarithmic
expressionsexpressions
Property 1
Property 3
Property 2
Properties 1 and 3
Contracting logarithmic Contracting logarithmic
expressionsexpressions
Property 3
Property 1
Properties 3 and 2
Property 1
•stop
