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 26. 62 = 36 27. 2891/2 = 17 28. 14-2 = 1/196 29. 34 = 81 30. 3y = 9 31. 83 = x 32. e4 = x 33. ey = 9 34. e1/2 = x 35. log9 81 = 2 36. log1/4 1/64 = 3 37. log10 0.001 = -3 38. log64 8 = ½ 39. log1/12 1/144 = 2 40. log9 1/81 = -2 41. ln 2 = x 42. ln y = 3 43. ln ½ = x

7.4 – Properties of Logarithms

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

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

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

Part 1: Expanding Logarithms

4x Expand log y

x4 Expand log 729

Expand log m2n5

Expand log3 (2x)2

a2 b3 Expand log c4

Homework Worksheet questions 44 – 55

Part 2: Condensing Logarithms

Properties of Logarithms… Product Property Quotient Property Power Property

Write log4 32 - log4 2 as a single logarithm

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

Condense log 8 – 2 log 6 + log 3

Condense log3 4 – log3 y – log38x

Part 3: Change of Base Formula

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

Use the change of base formula to solve log81 27

Use the change of base formula to solve log5 36

Use the change of base formula to solve log8 32

Use the change of base formula to solve log4 18

Homework Worksheet questions 56 – 73