Properties of Logarithms
Change-of-Base
Since most calculators only have two types of log keys, one for common logarithm (base 10) and one for natural logarithms (base e), you may use the Change-of-Base Formula.
Then
can be converted to a different base using any of the following formulas:
- Base b
- Base 10
- Base e
Changing Bases Using Common Logarithms
Changing Bases Using Natural Logarithms
The Properties of Logarithms
Let a be a positive number such that
and let n be a real number. If u and v are positive real numbers, the following properties are true:
Example:


Example:
Example:
Rewriting Logarithmic Expressions
To expand a logarithmic expression you must use the logarithmic properties to make the expression as "stretched out" as possible.
Expanding the Logarithm of a Product
Expanding the Logarithm of a Quotient
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To condense a logarithmic expression you must make the expression as simplified as possible by using the properties.
Condensing a Logarithmic Expression
Works Cited
Larson, Ron, Robert P. Hostetler, Bruce H. Edwards, and David E. Heyd.Precalculus with Limits: A Graphing Approach. Boston: Houghton Mifflin, 1997. Print.
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