Name ______Date ______Period ______
Review #16- Logarithms
Solve algebraically.
1. 5(23x) = 82. ex+3 = πx
3. 5x-2 = 33x+24. x4/3 = 10
5. log46. 32x– 2(3)x = 8
Applications.
- How long will it take for $100 to become $1000 if it is invested at 8% compounded:
a) annually b) quarterlyc) continuously
- A fossilized piece of wood is found to contain 30% of the normal level of carbon-14 present when a tree of this type is alive. Estimate the age of the fossil. (The half-life of carbon-14 is 5730 years. Round to the nearest year.)
9. A pond is seeded with a small type of prolific fish. The number of fish after t months can be estimated by the following equation:
a)How many fish were present initially?
b) When will the population of fish reach 2000?
10. The consumption of cola in the United States follows the continuous growth model. The amount consumed is measured in billions of gallons per year and t is years since 1980. The consumption rate doubles every 5 years with a rate of 6 billion gallons per year in 1980.
a) Write the model for the consumption of cola (in billions of gallons) in year t since
1980.
b) According to the model, what was the consumption rate for the year 1987?
c) When would the rate exceed 150 billion gallons per year?
Graph by hand and solve using a graphing calculator.
11. ln x = x2 – 2x = ______12. ex = x = ______
Rewrite each log expression in exponential form. Rewrite each exponential expression in log form.
13. log 45 = x ______14. e-3 = ______
15. loga16 = 4 ______16. 9½ = 3 ______
Evaluate.
17. 103log5 = ______18. ln e-⅔ = ______19. = ______
20. log21 = ______21. ln (-12) = ______22. log7= ______
23. = ______24. log5= ______
Use the properties of logarithms to expand as much as possible.
25. log 26. log3 54
27. 28.
Use the properties of logarithms to condense as much as possible.
29. 3log2x + 30. log (x2 – 9) − log (x2 + 7x + 12)
31. 2ln12 – ln 6 + ln 3 – 5 ln232. log43 + log4(4 − x2) – log4x
33. e2ln3+ln534. 2log2 3 – log2 72
Solve each equation for x.
35. log236. log (x− 1) = log (x+ 1) − log (x + 2)
37. 26-x = 42+x38.
CATALOG CARD REVIEW.
Note: The questions below are examples of the type that will be asked on the test. You need to study all of your catalog cards, however, and know all material covered on them. The parent functions and their characteristics are on the function chart (A 9-8).
39. Is the function an even function, an odd function, or neither?
______
40. What is the range of the function f(x) = x2 ? ______
41. Are the following sets of points symmetric about the x-axis, the y-axis, the origin, or y = x?
{(-2, 3), (5, 4), (-1, -3), (0, 4)} and {(2, 3), (-5, 4), (1, -3), (0, 4)} ______
42. Start with the graph of y = x2. Stretch it by a factor of 2 in the y direction, shift it to the right 3 units and down 5 units. The new function is f(x) = ______
43. Which of the following functions are one-to-one?______
a) d) f(x) = x3
b)f(x) = x2e)
c)f(x) = xf)
44. Supply the following information about the rational function.
Domain: ______VA:______
x-intercept(s)______HA:______
y-intercept:______SA:______
Hole(s): ______
45. Write the equation for the asymptote of each function.
f(x) = 2x______
f(x) = log2x______
______
Answers to Review #16
1. .226
2. 20.728
3. -3.212
4. ±5.623
5. , -22
6. 1.262
7. a) 29.919 years
b) 29.069 years
c) 28.782 years
8. 9952.813 years
9. a) P(0) = 4 fish
b) 14.101 months
10. a) A(t) =
b) A(7) = 15.875
billion gallons
c) in 2003
(23.157 years)
11. .138, 1.564
12. -3.981, 1.074
13. 45 = 10x
14.
15. 16 = a4
16. log93 = ½
17. 125
18. -⅔
19. -⅓
20. 0
21. Not Possible
22. ½
23.
24. -3
25. log5 – log3 – 2logx
26. log32 + 3
27. 6log2x + log2y
28. lnx +ln(x2+1)
–ln(x–2)
29. log2x
30. log
31. ln
32. log4
33. 45
34. -3
35. 8
36.
37. ⅔
38. -2, 1
39. Even
40. [0, )
41. y-axis
42. f(x) = 2(x-3)2 – 5
43. a, c, d, f
44. D: x ≠ 4, -1
Xint: (-5, 0)
Yint:
Hole:
VA: x = 4
HA: y = 1
No SA
45. y = 0
x = 0
x = 0 and y = 0
Answers to Review #16
1. .226
2. 20.728
3. -3.212
4. ±5.623
5. , -22
6. 1.262
7. a) 29.919 years
b) 29.069 years
c) 28.782 years
8. 9952.813 years
9. a) P(0) = 4 fish
b) 14.101 months
10. a) A(t) =
b) A(7) = 15.875
billion gallons
c) in 2003
(23.157 years)
11. .138, 1.564
12. -3.981, 1.074
13. 45 = 10x
14.
15. 16 = a4
16. log93 = ½
17. 125
18. -⅔
19. -⅓
20. 0
21. Not Possible
22. ½
23.
24. -3
25. log5 – log3 – 2logx
26. log32 + 3
27. 6log2x + log2y
28. lnx + ln(x2 + 1)
– ln(x – 2)
29. log2x
30. log
31. ln
32. log4
33. 45
34. -3
35. 8
36.
37. ⅔
38. -2, 1
39. Even
40. [0, )
41. y-axis
42. f(x) = 2(x-3)2 – 5
43. a, c, d, f
44. D: x ≠ 4, -1
Xint: (-5, 0)
Yint:
Hole:
VA: x = 4
HA: y = 1
No SA
45. y = 0
x = 0
x = 0 and y = 0