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In Try This 1 you may have determined the following patterns. They are called the laws of logarithms.
LAWS OF LOGARITHMS |
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Law of Logarithms |
Law Expressed Mathematically |
Comparison Between Law of Logarithm and Law of Powers |
Product Law of Logarithms |
logb (M × N) = logb M + logb N |
(bm)(bn) = bm+n
logb (M × N) = logb M + logb N
Note that multiplying terms in a logarithm or powers is equal to the sum of the logarithms or exponents. |
Quotient Law of Logarithms |
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Note that dividing terms in a logarithm or powers is equal to the difference between the logarithms or exponents. |
Power Law of Logarithms |
logb (Mn) = nlogb M |
logb (Mn) = nlogb M
Note that a power in a logarithm or a power to a power is equal to the product of the power and the logarithm or the exponents of the power. |
Open Properties of Logarithms to see how the laws of logarithms can be derived. Choose the Tutorial button (
), and then select The Product Law of Logarithms. Work your way through the activities.
