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Published byClaire Franklin Modified 6 months ago

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22. $5,000e(0.069)(5) = $7,059.95 23. $20,000e(0.0375)(2) = $21,557.68 24. $2,000e(0.051)(3) = $2,330.65 25. $950e(0.06)(10) = $1,731.01 = /2 = = 1/ = 81 30. 3y = = x e4 = x ey = 9 34. e1/2 = x log9 81 = log1/4 1/64 = 3 37. log = log64 8 = ½ log1/12 1/144 = 2 40. log9 1/81 = ln 2 = x 42. ln y = ln ½ = x

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**7.4 – Properties of Logarithms**

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Simplify x2 x4 Simplify x5 ÷ x2 Simplify (x2)3

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If x = logb m and y = logb n, what is logb mn?

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**m n logb mn = logb m + logb n logb = logb m – logb n**

Properties of Logarithms… m > 0 n > 0 b≠ 1 Product Property logb mn = logb m + logb n Quotient Property m logb = logb m – logb n n Power Property logb mn = n logb m

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**Part 1: Expanding Logarithms**

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4x Expand log y

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x4 Expand log 729

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Expand log m2n5

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Expand log3 (2x)2

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a2 b3 Expand log c4

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Homework Worksheet questions 44 – 55

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**Part 2: Condensing Logarithms**

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**Properties of Logarithms…**

Product Property Quotient Property Power Property

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**Write log4 32 - log4 2 as a single logarithm**

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**Write 6 log2 x + 5 log2 y as a single logarithm**

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Condense log 8 – 2 log 6 + log 3

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**Condense log3 4 – log3 y – log38x**

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**Part 3: Change of Base Formula**

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**logc m logb m = logc b Change of Base Formula…**

For any positive numbers m, b, c, with b ≠ 1 and c ≠ 1: logc m logb m = logc b

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**Use the change of base formula to solve log81 27**

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**Use the change of base formula to solve log5 36**

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**Use the change of base formula to solve log8 32**

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**Use the change of base formula to solve log4 18**

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Homework Worksheet questions 56 – 73

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