1. 3.3 Properties of Logarithms Change of Base

2. When solve for x and the base is not 10 or e. We have changed the base from b to 10. WE can change it to any base. So

3. Properties of Logarithms Log b (xy) = log b x + log b y Log b (x/y) = Log b x – Log b y Log b x k = k(log b x)

4. Expanding Logarithm Log 3 (6x) 4 y 7 z -2 = Log 3 (6x) 4 + Log 3 y 7 + Log 3 z -2 = 4 Log 3 6x + 7Log 3 y - 2 Log 3 z = 4 Log 3 6 + 4 Log 3 x +7Log 3 y - 2 Log 3 z

5. Expanding Logarithm Log 3 (6x) 4 y 7 z -2 = Log 3 (6x) 4 + Log 3 y 7 + Log 3 z -2 = 4 Log 3 6x + 7Log 3 y - 2 Log 3 z = 4 Log 3 6 + 4 Log 3 x +7Log 3 y - 2 Log 3 z

6. Expanding Logarithm Log 3 (6x) 4 y 7 z -2 = Log 3 (6x) 4 + Log 3 y 7 + Log 3 z -2 = 4 Log 3 6x + 7Log 3 y - 2 Log 3 z = 4 Log 3 6 + 4 Log 3 x +7Log 3 y - 2 Log 3 z

7. Condensing Logarithm ⅓ [4 ln(x – 2) + ln x – ln(x 2 – 1)] ⅓ [ln(x – 2) 4 + ln x – ln(x 2 – 1)] ⅓ [ln x(x – 2) 4 – ln(x 2 – 1)] = =

8. Homework Page 223 -224 #1, 12, 16, 22, 26, 28, 31, 34, 38, 42, 45, 50, 54, 57, 64, 71, 74, 80, 83, 86, 100, 103

9. Homework Page 223 -224 #9, 13, 19, 23, 29, 33, 36, 39, 48, 52, 55, 61, 67, 73, 75, 82, 97, 102, 106