1. 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

2. 7.4 – Properties of Logarithms

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

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

5. 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

6. Part 1: Expanding Logarithms

7. 4x
Expand log y

8. x4
Expand log
729

9. Expand log m2n5

10. Expand log3 (2x)2

11. a2 b3
Expand log c4

12. Homework
Worksheet questions 44 – 55

13. Part 2: Condensing Logarithms

14. Properties of Logarithms…
Product Property
Quotient Property
Power Property

15. Write log4 32 - log4 2 as a single logarithm

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

17. Condense log 8 – 2 log 6 + log 3

18. Condense log3 4 – log3 y – log38x

19. Part 3: Change of Base Formula

20. 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

21. Use the change of base formula to solve log81 27

22. Use the change of base formula to solve log5 36

23. Use the change of base formula to solve log8 32

24. Use the change of base formula to solve log4 18

25. Homework
Worksheet questions 56 – 73