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Level 407

Logarithmic Functions


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Definition of the logarithmic function
Where a is a positive number not equal to 1, the logarithmic function with base a =
Properties of logarithms #1
We must raise a to the power of 0 to get 1
Properties of logarithms #2
We must raise a to the power of 1 to get a
Properties of logarithms #3
We must raise a to the power of x to get a^x
Properties of logarithms #4
logaX is the power to which a must be raised to get x
Graphs of logarithmic functions
If a one to one function has domain A and range B, then its inverse function f^-1 has domain B and range A
common logarithms
The logarithm with base 10 is called the common logarithm and is denoted by omitting the base
Natural logarithm
The logarithm with base e is called the natural logarithm and is denoted by "ln"
Properties of natural logarithms #1
We must raise e to the power of 0 to get 1
Properties of natural logarithms #2
We must raise e to the power of 1 to get e
Properties of natural logarithms #3
We must raise e to the power of x to get e^x
Properties of natural logarithms #4
ln X is the power to which e must be raised to get x
logaX=Y
Logarithmic Form
a^Y=X
Exponential Form
Domain: all positive real numbers, never zero
What are the critical characteristics of the logarithmic function? Describe in detail, discussing domain, range, intercepts, asymptotes and end behavior.
What is the domain of a logarithmic function?
The domain is all real numbers except for regions where the expression is undefined, in the example of logarithms that would be when a log is less than or equal to zero