07.03 Notes.docx

# Log 7 40 log 7 8 log 7 5 notice that the base of each

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log 7 40 − log 7 8 = log 7 5 Notice that the base of each logarithm in the equation is 7. What operation is performed on the arguments 40 and 8 to result in the argument 5? Division. If two or more logarithmic expressions with the same base are subtracted, divide the first argument by the second argument to find the difference. This is called the Quotient Property of Logarithms. You can confirm this difference by using the Change of Base Formula. The Quotient Property of Logarithms may be summarized with the following algebraic equation.

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Quotient Property of Logarithms log b x − log b y = log b Notice that the argument of the logarithmic term following the subtraction sign will be in the denominator! Power Property of Logarithms Addition of logarithms with like bases involves the multiplication of arguments. Subtraction of logarithms with like bases involves the division of arguments. log 7 2 3 = 3 log 7 2 What is happening to the exponent on the argument of 2 from one side of the equation to the other? The exponent (3) on the argument (2) becomes a coefficient of the logarithmic expression. A coefficient of a logarithmic term can be moved to the exponent of its argument and vice versa. This is called the Power Property of Logarithms.
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