1. Exponential and Logarithmic
Practice Quest 1

2. 1)Graph y = 5 x - 2 + 3 1. Inc/Dec Inc 2. Hor/Vert; Key Point
3. Domain:
D: 
4. Range:
R: (3, ∞)
5. Equation of asymp.
y = 3 y x 5 -5

3. 2)Graph y = log .3 (x) – 1 1. Inc/Dec Dec 2. Hor/Vert; Key Point
1↓; (1, -1)
3. Domain:
D: (0, ∞)
4. Range:
R: 
5. Equation of asymp.
x = 0 y x 5 -5

4. Graph y = log e (x – 5) + 2 1. Inc/Dec Inc 2. Hor/Vert; Key Point
3. Domain:
D: (5, ∞)
4. Range:
R: 
5. Equation of asymp.
x = 5 y x 5 -5

5. Get same bases; set exponents =

6. Get same bases; set exponents =

7. If y = b x , then log b y = x logbaseanswer =exp, baseexp = answer
12) log 27 x = 1/3
271/3 = x
(3 3)1/3= x
x = 3
13) logx64= 3/2
x3/2 = 64
(x3/2)2/3 = (26)2/3
x = 24
x = 16
14) log e e5 = x
e5 = ex
x = 5
9) log = x
3 x = 243
3 x = 35
x = 5
10) log264 = x
2x = 64
2x = 26
x = 6
11) log 7 1 = x
7x = 1
x = 0

8. If y = b x , then log b y = x logbaseanswer =exp, baseexp = answer
log3 27 = x
(3½)x = 33
½x = 3
x = 6
log x5 = 1/3
x1/3 = 5
(x1/3)3 = 53
x = 125
15) log 5 x = - 4
5-4 = x
x = 1/625
16) log x ¼ = -2/3
x -2/3 = ¼
(x-2/3)-3/2 = (2-2)-3/2
x = 23
x = 8
log5x = 0
50 = x
x = 1

9. log 8 3 x2y 17) Expand ( )( log 8 + log 8 ) ( )( log 8 x + log 8 y )

10. log 5 (x2y)/ 2c 18)Expand log 5 x + log 5 y – log 5 2– log5 c
log log 5 – log 5 – log5
log 5 x + log 5 y – log 5 2– log5 c
2log5 x +½log5 y – log5 2– log5 c

11. 19)Write as one log:
log 7y – 2log x + ½ log c
log (7yc ) x2

12. 20) Write as one log:
(1/3)(log 2x2 + log 3y)
log ( 6x2y)
log (36x2y)