Precalculus Review Worksheet for second Chapter 4 test _____________
name
For the test, you must know the exponential growth equations. They will not be provided for you. Very specific formulas, like
Newton’s law of cooling, will be provided.
t
a. A (t) = A0 (1 + r)t
c. A (t) = A0 ert
b. A (t) = A0 b k
You also must know the laws of logarithms. They will not be provided to you. Remember
M
d. log b MN = log b M + log b N
e. log b
= log b M  log b N
f. log b Mk = k log b M
N
logbx = a IFF ba = x
log c ln c log a c


g. log bc =
log b ln b log a b
The test will have 2 pages. On the first page, you will not be able to use a calculator. On the second, you will.
I. Simplify the following expressions, if possible. Answers to log problems should be exact - either in fractional or radical form. Get
the answer w/out a calculator!
1.
log 1000
2. log .001
6. ln e2
10.
7. ln
1
ln 25  ln 2
2
14. ln e3
19. log3 3 81
3. log 3 81
1
8.
e3
4. log 5 .04
9. log 3 + log 6  log 2
log 5 2 + log 5 3
11. 2 log P  log Q
12. log b M + log b N  3 log b P
15. ln e5y
16. 10log 6
20. log(log 100100)
*21. log4(log228)
17. 10 2+logx
*22.
5. log 7 ( 7 3 7 )
log 4 32
log 8 16
13. ln c +
1
ln d
3
18. 10 4log2
*23. If logbM = 3, then logMb = ?
II. Solve for x. Try not to use a calculator. Leave answers in exact form.
24. log x = 5
25. x3 = 20
26.
log | x | = 2
27. ln ( ln x ) = 2
28. log 5 ( log 4 x ) = 0
29. log 3 ( log 5 x ) = 1
30.
(log x)3 = 27
31. 3x+1 = 62x
(*problems taken from math team competitions)
32. log 5 x + log 5(x  4) = 1
33. log 3( x + 1 ) + log 312 = 4
34. log 9 (x2 + 12) = log 9 x + log 9 7
35. log (3x  1)  log (2x + 5) = 2
36. 32x  11  3x  12 = 0
37.
38. 3x = 26
39.
e x = 70
e2x  8ex + 15 = 0
40. 52x = 100
III. Solve the following word problems
41. An investment is made at 5.75% compounded quarterly. How long does it take to double the investment?
42. If an investment of $1000 is compounded continuously, what interest rate must you get to triple the money in 12 years? (round to
hundredth of a percent)
43. Uranium 238 has a half life of 4.5 billion years (!!). How long will it take 1 kg to decay to 1 g?
44. How long does it take $500 to become $2000 if it is invested at 3.25% and compounded a) yearly b) continuously ?
45. Decibel Level is found by using this formula dB = 10 log
I
.
I0
What is the decibel level of 3 stereos, each playing at 72 dB?
46. The population of a certain country was 2,345,235 in 1985 and 3,458,377 in 1995. Assume that the growth is exponential. (a) Find
a formula for the population t years after 1985. (b) Find the time required for the population to double. (b) Use the data to predict the
population in the year 2005.
47. A kettle full of water is brought to a boil in a room with temperature 32° C. After 5 minutes the temperature of the water has
decreased from 100° C to 80°C. Find the temperature after another 5 minutes.
48. A substance has a hydrogen ion concentration of [ H+ ] = 2.1 * 10-2 M. Find the pH of the substance.