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3.3 Properties of Logarithms

3.3 Properties of Logarithms. Change of Base. 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

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3.3 Properties of Logarithms

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  1. 3.3 Properties of Logarithms Change of Base

  2. 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

  3. Properties of Logarithms Logb (xy) = logb x + logby Logb(x/y) = Logbx – Logby Logb xk = k(logb x)

  4. Expanding Logarithm Log3 (6x) 4 y 7 z -2 = Log3 (6x)4 +Log3 y7+ Log3 z -2 = 4 Log3 6x + 7Log3y - 2 Log3z = 4 Log3 6 + 4 Log3x+7Log3y - 2 Log3z

  5. Expanding Logarithm Log3 (6x) 4 y 7 z -2 = Log3 (6x)4 +Log3 y7+ Log3 z -2 = 4 Log3 6x + 7Log3y - 2 Log3z = 4 Log3 6 + 4 Log3x+7Log3y - 2 Log3z

  6. Expanding Logarithm Log3 (6x) 4 y 7 z -2 = Log3 (6x)4 +Log3 y7+ Log3 z -2 = 4 Log3 6x + 7Log3y - 2 Log3z = 4 Log3 6 + 4 Log3x+7Log3y - 2 Log3z

  7. Condensing Logarithm ⅓ [4 ln(x – 2) + ln x – ln(x2 – 1)] ⅓ [ln(x – 2)4 + ln x – ln(x2 – 1)] ⅓ [ln x(x – 2)4– ln(x2 – 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

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