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Home : Math & Science : Math Study Guides : Algebra II : Logarithmic Functions : Properties of Logarithms
Properties of Logarithms
Properties of Logarithms
Logarithms have the following properties:
Since a0 = 1 and a1 = a:
Property A: loga1 = 0
Since ax and logax are inverses:
Property B: logaa = 1
Property C: logaax = x
Since apaq = ap+q and Property D: alogax = x = ap-q:
Property E: loga(pq) = logap + logaq
Since loga(Mn) = loga(M·M·M ... M) = logaM + logaM + logaM + ... + logaM = n·logaM
Property F: loga( ) = logap - logaq
Property G: loga(Mn) = n·logaM
Property H
Logarithms have an additional property, called property H, and a property H1 that is a specific case of property H.
Property H: logaM =
, where b is any base.Property H1: logaM = ![]()
Applications of Properties
The numerous properties listed on this page can be used to evaluate logarithmic functions. Property
H1 is especially useful when evaluating logarithms with a calculator:
since most calculators only evaluate logarithms with base 10, we can evaluate
logaM by evaluating
. For example, log34 = .
Example: log510 + log520 - log58 =?
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