1. 8-4 Properties of Logarithms
10/25/17

2. 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.)

3. 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”

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

5. 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 =
log log5 y = (Power Prop.)
log5 81y = (Product Prop.)

6. Assignment: pg 449 #1 – 18