1. Quest Review Unit 2

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 = 5/3 4. 9 x = 27 3 2x = 3 3 x = 3/2 5. 125 x = 25 5 3x = 5 2 x = 2/3 6. 4 x = 1/16 4 x = 4 -2 x = -2

3. Get same bases; set exponents = 7. 27 x = 1/81 3 3x = 3 -4 x = - 4/3 8. (½ ) x = 8 2 -x = 2 3 x = -3 9.  2 x = 1/8 2 (½)x = 2 - 3 ½ x = -3 x = -6 10. (¾) x = 9/16 (¾) x = (¾) 2 x = 2 11. 2 3x + 1 = ½ 2 3x + 1 = 2 -1 3x + 1= -1 3x = -2 x = -2/3 12. 27 2x+1 = 3 (3 3 ) 2x+1 = 3 1 6x+3=1 6x = -2 x = -1/3

4. If y = b x, then log b y = x log base answer =exp, base exp = answer 13. log 3 243 = x 3 x = 243 3 x = 3 5 x = 5 14. log 27 x = 1/3 27 1/3 = x (3 3 ) 1/3 = x x = 3 15. log 5 x = - 4 5 -4 = x x = 1/625 16. log  3 27 = x (3 ½ ) x = 3 3 ½x = 3 x = 6 17. log 2 64 = x 2 x = 64 2 x = 2 6 x = 6 18. log x 64= 3/2 x 3/2 = 64 (x 3/2 ) 2/3 = (2 6 ) 2/3 x = 2 4 x = 16

5. If y = b x, then log b y = x log base answer =exp, base exp = answer 19. log x ¼ = -2/3 x -2/3 = ¼ (x -2/3 ) -3/2 = (2 -2 ) -3/2 x = 2 3 x = 8 20. log x 5 = 1/3 x 1/3 = 5 (x 1/3 ) 3 = 5 3 x = 125 21. log 7 1 = x 7 x = 1 x = 0 22. log e e 5 = x e 5 = e x x = 5 23. log 5 x = 0 5 0 = x x = 1

6. 24. Graph y = 5 x - 2 + 3 1. Inc 2. 2 R, 3↑; (2, 4) 3. D:  4. R: (3, ∞) 5. y = 3 y x 5 5 -5

7. 24. Graph y = 5 x - 2 + 3 1. Inc 2. 2 R, 3↑; (2, 4) 3. D:  4. R: (3, ∞) 5. y = 3 y x 5 5 -5

8. 25. Graph y = log.3 (x) – 1 1. Dec 2. 1↓; (1, -1) 3. D: (0, ∞) 4. R:  5. x = 0 y x 5 5 -5

9. 25. Graph y = log.3 (x) – 1 1. Dec 2. 1↓; (1, -1) 3. D: (0, ∞) 4. R:  5. x = 0 y x 5 5 -5

10. 26. Graph y = log e (x – 5) + 2 1. Inc 2. 5 R, 2↑; (6, 2) 3. D: (5, ∞) 4. R:  5. x = 5 y x 5 5 -5

11. 26. Graph y = log e (x – 5) + 2 1. Inc 2. 5 R, 2↑; (6, 2) 3. D: (5, ∞) 4. R:  5. x = 5 y x 5 5 -5

12. 27. Expand log 8 3  x 2 y (1/3)(2log 8 x + log 8 y )

13. 28. Expand log 5 (x 2  y)/ 2c 2log 5 x +½ log 5 y – log 5 2– log 5 c

14. 29. Write as one log: log 7y – 2log x + ½ log c log (7y  c )/x 2

15. 30. Write as one log: (1/3)(log 2x 2 + log 3y) log ( 3  6 x 2 y )