Definition of Logarithmic Functions:
-
can also be written as 
...... they are equivalent.
The logarithmic function is called log base a
ex.
........ which is the same as........ 
Then solve for x....... which is 3
Properties of Logarithms:
1.
because 
2.
because 
3.
, then x = y ----------- One-to-One property
Transformations of Graphs of Logarithmic Functions:
The graphs of logarithms are the same as the graphs for exponents but they are reflected over the line of y = x.
The transformations for logarithmic graphs are the same as transformations for any other kinds of graphs.
The best way to show this is in an example.
Ex.
- The transformations for this graph are the same as for any other graph
- Moved to the right 1, and moved up 2.
Natural Logarithms:
The function is defined as:
, x > 0 This is called the natural logarithmic function.
Properties of Natural Logarithms:
1.
because 
2.
because 
3.
, the x=y ------ One-to-One Property
James Thomas
-
can also be written as ...... they are equivalent.The logarithmic function is called log base a
ex.
........ which is the same as........ Then solve for x....... which is 3
Properties of Logarithms:
1.
because 2.
because 3.
, then x = y ----------- One-to-One propertyTransformations of Graphs of Logarithmic Functions:
The graphs of logarithms are the same as the graphs for exponents but they are reflected over the line of y = x.
The best way to show this is in an example.
Ex.
- The transformations for this graph are the same as for any other graph
- Moved to the right 1, and moved up 2.
Natural Logarithms:
The function is defined as:
, x > 0 This is called the natural logarithmic function.Properties of Natural Logarithms:
1.
because 2.
because 3.
, the x=y ------ One-to-One PropertyJames Thomas
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