Types of LogaritmsAlthough a logarithm may be defined with any base, the logs most often encountered are the logarithm to the base 10 which is called the common logarithm and the logarithm to the base e which is called the natural logarithm. Base changes can be accomplished. For a chosen base: Logarithms may be manipulated with the combination rules. 
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Logarithm CombinationsThe logarithm to the base b of the variable x is defined as the power to which you would raise b to get x. It is written The general combination properties of logarithms are: 
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Logarithm Base ChangeIf the logarithm to the base a is known, then the logarithm to the base b can be obtained by the base change relationship: This can be proved from the definition and combination rules for logarithms. If then and rearranging gives The most common base changes are from the natural log to base 10 log or vice versa. 
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What is a Logarithm?The logarithm to the base b of the variable x is defined as the power to which you would raise b to get x. If the logarithm to the base b of x is equal to y, then b raised to the y power will give you the value x. It it written The general combination properties of logarithms are: 
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