# Quest Review.ppt by malj

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```									Quest Review

Unit 2
Get same bases; set exponents =
1.   2x = 128       4.  9x = 27
2x = 2 7           32x = 33
x=7                x = 3/2
2. Ö3x = 243        5. 125 x = 25
31/2x = 35            53x = 52
1/2x = 5                x = 2/3
x = 10        6.    4x = 1/16
3. 8x = 32               4x = 4-2
23x = 25               x = -2
x = 5/3
Get same bases; set exponents =
x                   (¾)x= 9/16
7.  27 = 1/81       10.
(¾)x= (¾)2
33x = 3-4                 x=2
x = - 4/3    11. 23x + 1 = ½
8. (½ )x = 8             23x + 1 = 2-1
3x + 1= -1
2-x = 23                3x = -2
x = -3                 x = -2/3
9. Ö2x = 1/8        12. 272x+1 = 3
(33)2x+1 = 31
2(½)x= 2- 3           6x+3=1
½ x = -3                 6x = -2
x = -6                 x = -1/3
x
If y = b , then log b y = x
exp
13. log 3 243 = x        16. logÖ3 27 = x
3 x = 243           (3½)x = 33
½x = 3
3 x = 35
x=6
x=5         17. log264 = x
14. log 27 x = 1/3                 2x = 64
271/3 = x                  2 x = 26
(3 3)1/3= x                  x=6
x=3         18. logx64= 3/2
x3/2 = 64
15.   log 5 x = - 4
(x3/2)2/3 = (26)2/3
5-4 = x                  x = 24
x = 1/625               x = 16
If y = b , then log b y = x
exp
19. log x ¼ = -2/3
x -2/3 = ¼             22. log e e5 = x
(x-2/3)-3/2 = (2-2)-3/2             e 5 = ex
x = 23                         x=5
x=8
20. log x5 = 1/3               23.    log5x = 0
x1/3 = 5                         50 = x
(x1/3)3 = 53                         x=1
x = 125
21. log 7 1 = x
7x = 1
x=0
x -2
24.                    Graph y = 5             +3
1.   Inc                    5
y

2.   2 R, 3↑; (2, 4)
3.   D:                                   x

4.   R: (3, ∞)
-5

5.   y=3
-5        5
x -2
24.              Graph y = 5               +3
1.   Inc               5
y

2.   2 R, 3↑; (2, 4)
3.   D:                               x

4.   R: (3, ∞)
-5

5.   y=3
-5        5
25.              Graph y = log .3 (x) – 1
1. Dec                          y
5

2. 1↓; (1, -1)
3. D: (0, ∞)                            x

4. R: 
-5

5. x = 0                   -5       5
25.          Graph y = log .3 (x) – 1
1. Dec                       y
5

2. 1↓; (1, -1)
3. D: (0, ∞)                         x

4. R: 
-5

5. x = 0                -5       5
26. Graph y = log e (x – 5) + 2
1.   Inc                      y
5

2.   5 R, 2↑; (6, 2)
3.   D: (5, ∞)                        x

4.   R: 
-5

5.   x=5                 -5       5
26. Graph y = log e (x – 5) + 2
1.   Inc                      y
5

2.   5 R, 2↑; (6, 2)
3.   D: (5, ∞)                        x

4.   R: 
-5

5.   x=5                 -5       5
27.                  Expand

log 8 Ö x y
3      2
(1/3)(2log 8 x + log 8 y )
28.                 Expand
log 5 (x Öy)/ 2c
2
2log 5 x +½ log 5 y – log 5 2– log5 c
29.      Write as one log:
log 7y – 2log x + ½ log c
2
log (7yÖc )/x
30.     Write as one log:
2
(1/3)(log 2x + log 3y)

log ( Ö6x y)
3       2

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