quest review unit 2. get same bases; set exponents = 1. 2 x = 128 2 x = 2 7 x = 7 2. 3 x = 243 3...

Quest Review Unit 2

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Quest Review

Unit 2

Get same bases; set exponents =

1. 2x = 128

2x = 27

x = 7

2. 3x = 243

31/2x = 35

1/2x = 5

x = 10

3. 8x = 32

23x = 25

x = 5/3

4. 9x = 27

32x = 33

x = 3/2

5. 125 x = 25

53x = 52

x = 2/3

6. 4x = 1/16

4x = 4-2

x = -2

Get same bases; set exponents =

7. 27x = 1/81 33x = 3-4

x = - 4/3

8. (½ )x = 82-x = 23

x = -39. 2x = 1/8 2(½)x= 2- 3

½ x = -3 x = -6

10. (¾)x= 9/16 (¾)x= (¾)2

x = 2 11. 23x + 1 = ½ 23x + 1 = 2-1

3x + 1= -1 3x = -2 x = -2/3 12. 272x+1 = 3 (33)2x+1 = 31

6x+3=1 6x = -2 x = -1/3

Page 4: Quest Review Unit 2. Get same bases; set exponents = 1. 2 x = 128 2 x = 2 7 x = 7 2. 3 x = 243 3 1/2x = 3 5 1/2x = 5 x = 10 3. 8 x = 32 2 3x = 2 5 x

If y = b x , then log b y = xlogbaseanswer =exp, baseexp = answer

13. log 3 243 = x 3 x = 243

3 x = 35

x = 5

14. log 27 x = 1/3 271/3 = x (3 3)1/3= x x = 3

15. log 5 x = - 4 5-4 = x x = 1/625

16. log3 27 = x (3½)x = 33

½x = 3 x = 6

17. log264 = x 2x = 64 2x = 26

x = 6

18. logx64= 3/2 x3/2 = 64 (x3/2)2/3 = (26)2/3

x = 24

x = 16

Page 5: Quest Review Unit 2. Get same bases; set exponents = 1. 2 x = 128 2 x = 2 7 x = 7 2. 3 x = 243 3 1/2x = 3 5 1/2x = 5 x = 10 3. 8 x = 32 2 3x = 2 5 x

If y = b x , then log b y = xlogbaseanswer =exp, baseexp = answer

19. log x ¼ = -2/3 x -2/3 = ¼

(x-2/3)-3/2 = (2-2)-3/2

x = 23

x = 8

20. log x5 = 1/3 x1/3 = 5 (x1/3)3 = 53

x = 125

21. log 7 1 = x 7x = 1 x = 0

22. log e e5 = x

e5 = ex

x = 5

23. log5x = 0

50 = x

x = 1

Page 6: Quest Review Unit 2. Get same bases; set exponents = 1. 2 x = 128 2 x = 2 7 x = 7 2. 3 x = 243 3 1/2x = 3 5 1/2x = 5 x = 10 3. 8 x = 32 2 3x = 2 5 x

24. Graph y = 5 x - 2 + 3

1. Inc

2. 2 R, 3↑; (2, 4)

3. D: 4. R: (3, ∞)

5. y = 3

-5-5

Page 7: Quest Review Unit 2. Get same bases; set exponents = 1. 2 x = 128 2 x = 2 7 x = 7 2. 3 x = 243 3 1/2x = 3 5 1/2x = 5 x = 10 3. 8 x = 32 2 3x = 2 5 x

24. Graph y = 5 x - 2 + 3

1. Inc

2. 2 R, 3↑; (2, 4)

3. D: 4. R: (3, ∞)

5. y = 3

-5-5

Page 8: Quest Review Unit 2. Get same bases; set exponents = 1. 2 x = 128 2 x = 2 7 x = 7 2. 3 x = 243 3 1/2x = 3 5 1/2x = 5 x = 10 3. 8 x = 32 2 3x = 2 5 x

25. Graph y = log .3 (x) – 1

1. Dec

2. 1↓; (1, -1)

3. D: (0, ∞)

4. R:

5. x = 0

-5-5

Page 9: Quest Review Unit 2. Get same bases; set exponents = 1. 2 x = 128 2 x = 2 7 x = 7 2. 3 x = 243 3 1/2x = 3 5 1/2x = 5 x = 10 3. 8 x = 32 2 3x = 2 5 x

25. Graph y = log .3 (x) – 1

1. Dec

2. 1↓; (1, -1)

3. D: (0, ∞)

4. R:

5. x = 0

-5-5

Page 10: Quest Review Unit 2. Get same bases; set exponents = 1. 2 x = 128 2 x = 2 7 x = 7 2. 3 x = 243 3 1/2x = 3 5 1/2x = 5 x = 10 3. 8 x = 32 2 3x = 2 5 x

26. Graph y = log e (x – 5) + 2

1. Inc

2. 5 R, 2↑; (6, 2)

3. D: (5, ∞)

4. R: 5. x = 5

-5-5

Page 11: Quest Review Unit 2. Get same bases; set exponents = 1. 2 x = 128 2 x = 2 7 x = 7 2. 3 x = 243 3 1/2x = 3 5 1/2x = 5 x = 10 3. 8 x = 32 2 3x = 2 5 x

26. Graph y = log e (x – 5) + 2

1. Inc

2. 5 R, 2↑; (6, 2)

3. D: (5, ∞)

4. R: 5. x = 5

-5-5

Page 12: Quest Review Unit 2. Get same bases; set exponents = 1. 2 x = 128 2 x = 2 7 x = 7 2. 3 x = 243 3 1/2x = 3 5 1/2x = 5 x = 10 3. 8 x = 32 2 3x = 2 5 x

27. Expand

log 8 3 x2y(1/3)(2log 8 x + log 8 y )

Page 13: Quest Review Unit 2. Get same bases; set exponents = 1. 2 x = 128 2 x = 2 7 x = 7 2. 3 x = 243 3 1/2x = 3 5 1/2x = 5 x = 10 3. 8 x = 32 2 3x = 2 5 x

28. Expand

log 5 (x2y)/ 2c2log 5 x +½ log 5 y – log 5 2– log5 c

Page 14: Quest Review Unit 2. Get same bases; set exponents = 1. 2 x = 128 2 x = 2 7 x = 7 2. 3 x = 243 3 1/2x = 3 5 1/2x = 5 x = 10 3. 8 x = 32 2 3x = 2 5 x

29. Write as one log:

log 7y – 2log x + ½ log c

log (7yc )/x2

Page 15: Quest Review Unit 2. Get same bases; set exponents = 1. 2 x = 128 2 x = 2 7 x = 7 2. 3 x = 243 3 1/2x = 3 5 1/2x = 5 x = 10 3. 8 x = 32 2 3x = 2 5 x

30. Write as one log:

(1/3)(log 2x2 + log 3y)

log (36x2y)

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