8-4 Properties of Logarithms

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8-4 Properties of Logarithms

Presentation transcript:

8-4 Properties of Logarithms 10/25/17

The properties of logarithms remind me of the properties of exponents The properties of logarithms remind me of the properties of exponents. Those were: xa •xb = xa + b (Mult “means” add) xa ÷ xb = xa - b (Division “means” subtract) (xa)b = xab (Powers to powers “means” mult.)

The properties of logarithms: logb MN = logb M + logb N (Mult “means” add) “The Product Property” logb M/N = logb M - logb N (Div “means” sub) “The Quotient Property” logb Mx = x logb M (Powers to powers “means” mult) “The Power Property”

Examples: log2 (8•4) = log2 8 + log2 4 (Mult “means” add) log2 32 = 5; log2 8 = 3 and log2 4 = 2. 3 + 2 = 5 log3 (27/9) = log3 27 - log3 9 (Div “means” sub) log3 3 = 1; log3 27 = 3 & log3 9 = 2. 3 - 2 = 1 log2 82 = 2 log2 8 (Powers to powers “means” mult) log2 64 = 6; 2 log2 8 = 2•3 = 6

Write as a single log: log4 15–log4 3 = log4 15/3 = log4 5 (Quotient Prop.) log7 3 + log7 x = log7 3x (Product Prop.) 4log5 3 + log5 y = log5 34 + log5 y = (Power Prop.) log5 81y = (Product Prop.)

Assignment: pg 449 #1 – 18