Pre-Calculus Honors
Name
Chapter 3 Test REVIEW
Date
Simplify
1.
'
5.-25
- -
2.(2~ 1 -4- 1 )- 1
3. (2"1 + 4-1)'1
4. (3a~ 2 ) 3 • 3a5
6.10 2l °e 5
7.e3ln5
8.
Simplify by using fractional exponents or radicals.
10. Vx1
11.\25
f— V
12.92
is.
Solve.
14.8X = 26
15. 8^-1 = 2 x+1
16. 8* = 2 7 • 49
17. z 3 = 81
18. 3* = 81
19. 4* = 81
20.10* = 256
21. 25* = 2
Express in terms of log M and log Af.
23.1ogm 2 n
^r
n3
Express as a single logarithm.
24. Iog5 2 - !og5 3 _
25. In 4 + 2 In 3
26. A car bought in 2005 sold for $17,500. Today its value is $7200. What is the annual rate of decrease?
27. The half-life of Carbon-14 is 5730 years. If fish bones are supposed to have 12 mg of Carbon-14 per ounce and a
fossilized fish is found to have only 1 mg. of Carbon-14 per oz., how old is the fossil?
28. Write the exponential function through the points (0,4) and (2,2.25).
29. Determine the time necessary for an investment of $1,500 to quadruple if it is invested at a rate of 5.9%
compounded (a) annually, (b) monthly, (c) daily, and (d) continuously.
(a)
(b)
(c)
(d)
(a)
(b)
(c)
(d).
-
Solve for x.
30. s2* - y -1 = o
31.1og3(x + 3) +log 3 x = 4
32. Iog5
33. logs * >
34. Iog2 + logx 2 < 4
35. 32* - 5(3*) - 3 = -7
Sketch these graphs. Label: asymptotes, x and y intercepts.
36. /(x) = 2<*+3> - 7
37. /(x) = log(* - 2) + 3
38./O) = e~3x + 4
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