3.3 Properties of Logarithms Change of Base. 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.

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Presentation transcript:

3.3 Properties of Logarithms Change of Base

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

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)

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 Log 3 x +7Log 3 y - 2 Log 3 z

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 Log 3 x +7Log 3 y - 2 Log 3 z

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 Log 3 x +7Log 3 y - 2 Log 3 z

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)] = =

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

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