
11 ALGEBRA
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CHAPTER REVIEW TEST 3B
1. What is half of 4–19?
A) 2–39 |
B) 2–38 |
C) 2–37 |
D) 2–19 |
E) 2–18 |
2. Evaluate |
xy y x |
for x, y . |
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x y yx |
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x x |
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A) ( y) |
B) ( y) |
C) ( y) |
D) |
yx |
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3.A = 3x – 3–x and B = 3x + 3–x are given. Which of the following shows the relation between A and B?
A) A2 – B2 = 4 |
B) A2 – B = 2 |
C) A B = 4 |
D) B2 – A2 = 4 |
E) A2 + B2 = 4
4. Evaluate |
32x+1 (2 32x 1 )+(2 32 x ) |
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9x )+(4 9x 1) 32x |
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A) 5 |
B) 4 |
C) 3 |
D) 2 |
E) 1 |
2
5. Evaluate 2713 102.
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A) 45 |
B) 75 |
C) 100 |
D) 225 |
E) 450 |
6. Given |
5a – 3a = k, evaluate |
10a +6a |
in terms |
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50a – 18a |
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of k. |
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A) k2 |
B) k |
C) |
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k2 |
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7. Which statement is false?
A) 415 |
+ 415 |
= 231 |
B) 215 215 = 415 |
C) 215 |
+ 215 |
= 415 |
D) 2–15 > 0 |
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E) 415 215 = 245 |
8. Given 11443 = a, write |
11888 +11886 – 122 |
in terms |
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of a. |
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11443 – 1 |
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A) 122a |
B) 122a2 |
C) 122(a – 1) |
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D) 122(a + 1) |
E) a + 1 |
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9. Evaluate |
295 +294 +290 . |
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292 +291 +287 |
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A) |
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B) 1 |
C) 4 |
D) 8 |
E) 16 |
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10.If x y z 0, which of the following cannot be zero?
A) x2 + y2 + z |
B) x2 – y4 + z6 |
C) x + y + z |
D) (x + y + z)2 |
E) x2 + (y + z)2
Chapter Review Test 3B |
239 |

11. Evaluate |
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0.05 105 +3000 |
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0.005 104 0.01 103 |
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A) 100 |
B) 200 C) 400 D) 2000 E) 4000 |
12.a = 8100, b = 24340 and c = (0.008)–50 are given. Which statement is true?
A) c < a < b |
B) c < b < a |
C) a < b < c |
D) a < c < b |
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E) b < c < a |
13. Evaluate |
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7m 2 |
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72 m 1 |
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A) 1 |
B) 7m |
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C) 7m – 1 |
D) 72 |
E) –1 |
14.(0.08 0.2) = (a + 0.6) 10b is given where a, b . What is a possible value of a + b?
A) –3 |
B) –2 |
C) –1 |
D) 1 |
E) 2 |
15. Simplify |
ax |
ay |
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( ay )x y ( ax )x y. |
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A) ay |
B) a |
C) ax |
D) 1 |
E) ax – y |
16.How many consecutive zeros are there at the end of (75 12 5 8 40)4?
A) 13 |
B) 14 |
C) 15 |
D) 16 |
E) 17 |
17. Which function has the |
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graph shown opposite? |
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A) f(x) = 3x – 2 |
B) f(x) = 2x – 3 |
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C) f(x) = 3x – 2 |
D) f(x) = 3x – 3 |
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E) f(x) = 3x – 1 |
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18. |
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3 26 |
32–32 |
= 8n |
is given. Find n. |
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32–29 |
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A) –3 |
B) 5 |
C) 7 |
D) –4 |
E) 6 |
19. Evaluate |
( 5 – 1) |
(1+ |
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+ 3 |
5 ). |
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A) 3 |
B) 4 |
C) 5 |
D) 6 |
E) 7 |
20. Evaluate |
3 128 |
– 3 |
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3 250 |
– 3 |
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A) |
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C) 1 |
D) |
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E) |
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240 |
Algebra 11 |

CHAPTER REVIEW TEST 3C
1.What is the inverse of the logarithmic function f(x) = log2(x + 1)?
A) f –1(x) = 2x – 1 |
B) f –1(x) = 2x – 1 |
C) f –1(x) = 2x + 1 |
D) f –1(x) = 2x + 1 |
E)f –1(x) = 2x – 2
2.Which of the following points is on y=2+log3 x?
A) (2, 1) |
B) (2, 3) |
C) (3, 1) |
D) (3, 3) |
E) (9, 3) |
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3.What is the largest possible domain of f(x) = log4(2x + 1)?
A) |
(– |
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B) |
(– |
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C) |
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D) ( |
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E) |
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4. Which function has the |
y |
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graph shown opposite? |
2 |
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, 2) |
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(16 |
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A) f (x)= log 1 x |
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B) f (x)= log 1 |
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(2, -1 ) |
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C) f (x)= log 1 |
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D)f(x) = log2 x
E)f(x) = log4 x
5. Calculate log2 32. |
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A) 1 |
B) 2 |
C) 4 |
D) 5 |
E) 6 |
6. Solve |
log4 x= |
1 |
for x. |
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4 |
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A) ñ2 |
B) |
3 4 |
C) 4 2 |
D) 2 |
E) 6 |
7. logx 81 = –4 is given. What is x?
A) |
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B) |
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C) |
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D) 3 |
E) 9 |
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8. What is the logarithm of 125 to the base 5?
A) 5 |
B) 3 |
C) 2 |
D) 1 |
E) |
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3 |
9.Which of the following statements is/are true for the logarithmic function f(x) = log3 x?
I.f(x) is increasing for all x . II. f(x) has a range of +.
III. f(1) = 0
IV. f(3) = 3
A) I and II |
B) II and III |
C) I and III |
D) only III |
E) only II |
10.What is the largest possible domain of f(x) = logx(5x –7)?
A) (1, ) |
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B) (0, |
7 |
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C) (0, |
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D) |
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Chapter Review Test 3C |
241 |

11. Calculate log 10001 .
A) –4 |
B) –3 |
C) –2 |
D) 0.001 |
E) 2 |
12. Given that f(x) = log(2x – 1), what is f –1(2)?
A) |
103 |
B) 51 C) |
101 |
D) 50 E) |
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13. Which graph shows y = ln x? |
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A) |
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B) y |
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D) y |
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E)y
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0 1 e x
14. Given f(x) = ln x and (g f )(x) = x, find g(x).
A) 10x B) |
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C) |
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D) ex E) ex + 1 |
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ln x |
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15. Evaluate log 1000 – ln e2 – log4 64. |
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A) –3 |
B) –2 |
C) –1 |
D) 2 |
E) 3 |
16. log8 a = |
4 |
is given. Find a. |
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3 |
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A) 4 |
B) 8 |
C) 16 |
D) 28 |
E) 216 |
17. Which expression is equal to log x y2 ? z3
A)log x + 2 log y + 3 log z
B)log x + 2 log y – 3 log z
C)log(x + 2y – 3z)
D)log x + 2 log y – 13 log z
E)log x + 2 log y – log 3z
18.log 3 = a, log 5 = b and log 210 = c are given. Write log 7 in terms of a, b and c.
A) c – a – b |
B) c – a – 1 |
C) c – a – b + 1 |
D) c – a – b – 1 |
E)c – a + 1
19.Which expression is equal to ln 13 ?
A) |
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1 ln3 |
B) |
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1 ln3 |
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1 ln3 |
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D) |
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( ln3 – 1) |
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E) |
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( ln3 – 1) |
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20. Evaluate |
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log12 6 |
log8 6 |
log 4 6 |
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A) log6 3 |
B) log3 6 |
C) 0 |
D) 1 |
E) 2 |
242 |
Algebra 11 |

CHAPTER REVIEW TEST 3D
1. Evaluate log |
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2. |
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A) |
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B) |
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C) |
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D) |
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E) |
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2.log 2 = a and log 3 = b are given. What is log615 in terms of a and b?
A) |
b – a+1 |
B) |
a – b+1 |
C) |
a – b – 1 |
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a+ b |
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a+ b |
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a+1 |
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D) a – b – 1 |
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a+ b |
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a+ b+1 |
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3.A triangle ABC has sides a = log 4, b = log 20 and c = log 125. What is its perimeter?
A) 4 |
B) 5 |
C) 6 |
D) 7 |
E) 8 |
4. Evaluate log8 16 – log9 27 + logò10 – ln 4 e.
A) |
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B) |
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C) |
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D) |
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5. Which expression is equal to ln x + ln y – ln z?
A) ln(x + y – z) |
B) |
ln x+ y |
C) |
ln xy |
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D) ln(xy – z) |
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ln(x+ y) |
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ln z |
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6. Evaluate log6 9 |
+ log6 12 + log62. |
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A) 3 |
B) 6 |
C) 9 |
D) 10 |
E) 12 |
7. Calculate 9a if a = log |
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A) 81 |
B) 25 |
C) 15 |
D) 9 |
E) 13 |
8. Evaluate log7 8 log8 |
7 log7 10. |
A) log 7 B) ln 7 |
C) ln 10 D) log7 10 E) 1 |
9.Write 2log a + log b – log(a + 2b) as a single logarithm.
A) |
log |
a2 + b |
B) log |
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C) log |
2a+ b |
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a+2b |
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D) log(a – b) |
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log |
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10. What is the common logarithm of |
(0.4)2 |
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A) –2 |
B) –4 |
C) –6 |
D) –8 |
E) –10 |
Chapter Review Test 3D |
243 |

11.Calculate log 50 if log 2 = 0.301.
A) 1.701 B) 1.699 C) 1.30 D) 0.699 E) 0.602
12.a = 13.72 and b = 13720 are given. What is log a – log b?
A) –5 |
B) –4 |
C) –3 |
D) –2 |
E) 0.01 |
13. Evaluate |
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log24 30 |
log225 30 |
log 6 30 |
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E) 3 |
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14. Evaluate (a4 )loga2 3 . |
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A) 3 3 |
B) ñ3 |
C) 3 |
D) 3ñ3 |
E) 9 |
15. If |
log m n = x, what is |
log m m in terms of x? |
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D) –x – 1 |
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E) x + 1 |
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16.a = log2 5, b = log5 4 and c = log3 8 are given. Which statement is true?
A) b < a < c B) c < a < b C) b < c < a
D) c < b < a E) a < c < b
17. Evaluate log16 27 log125 32 log9 625.
A) |
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C) |
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D) |
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18.How many integer values of a satisfy the existence conditions for log7 – a (a + 9)?
A) 17 |
B) 16 |
C) 15 |
D) 14 |
E) 13 |
19. Which figure shows the graph y = 2–x + 1? |
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20. What is the inverse of f(x) = (0.2)–x + 1? |
A) f –1(x) = 1 + log x |
B) f –1(x) = 1 + log 5 |
5 |
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C) f –1(x) = log (x – 1) |
D) f –1(x) = log (x + 1) |
5 |
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E) f –1(x) = –1 + log5 x
244 |
Algebra 11 |

CHAPTER REVIEW TEST 3E
1. If loga b = logb c = logc a, what is |
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5. |
Given x = log |
3, calculate |
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3x |
– 2 |
–3x |
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loga c + logc a + logb a? |
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2x |
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A) 9 |
B) 4 |
C) 3 |
D) 2 |
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E) |
3 |
A) |
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B) 3 |
C) 5 |
1 |
D) |
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E) |
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2. Which function could have |
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the graph in the figure? |
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6. |
log3 2 = a is given. What is log4 6? |
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A) f (x)= log 1(x – 3) |
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B) f(x) = log3(x – 3) |
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C) f (x)= log 1(x – 3) |
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D)f(x) = log2(x – 3)
E)f (x)= –3+ log 1 x
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7. In |
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3. p = log2 9, q = log3 83 and r = log5 123 are given. |
shown opposite, |
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Which statement is true? |
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m( A) = (45 log6 y2)°, |
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A) p > r > q |
B) q > p > r |
C) r > q > p |
m( B) = (90 log6 x)° and |
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D) r > p > q |
E) q > r > p |
m( C) = (180 log6 ñz)°. |
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If logx z y = –3, what is y? |
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4. Which figure shows the graph y = 1 + log2 x? |
A) 36 |
B) 72 |
C) 144 |
D) 216 |
E) 256 |
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A) y |
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B) y |
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8. Which statement is false? |
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21 1 2 x |
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A) |
–1< log |
B) 1 < log 11 < 2 |
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C) |
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–3 < log |
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D) –3 < log 0.07 < –2 |
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E) 3 < log 2 |
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E)y
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9. Evaluate |
log |
1003 |
0.0001 . |
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0.012 |
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1 2 x |
A) 7 |
B) 8 |
C) 9 |
D) 10 |
E) 12 |
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Chapter Review Test 3E |
245 |

10.If log 2 0.301, how many digits are there in the number 254 816?
A) 22 |
B) 21 |
C) 20 |
D) 19 |
E) 18 |
11.If log(a + b) = log a + log b, what is a in terms of b?
A) |
b+1 |
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B) |
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b – 1 |
b+1 |
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12.f(x) = 3x – 2 and g(x) = log3(5x – 3) are given. What is p if (f g)(p) = 3?
A) 3 |
B) 5 |
C) 6 |
D) 9 |
E) 15 |
13.If log 72 = a and log 2 = b, what is log 3 in terms of a and b?
A) |
2a+ b |
B) |
a – 3b |
C) 3a – 2b |
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D) 2a + 3b |
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14. Evaluate |
2log9 2 . |
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A) 27 |
B) 18 |
C) 9 |
D) 6 |
E) 3 |
15. What is the largest possible domain of f (x) = 2 – log 3(x+4)?
A) (–4, 3] |
B) (3, 9] |
C) (–4, 5] |
D) (–3, 9] |
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16. Which function could |
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y |
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the graph in the figure? |
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1 |
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-2 -3 -1 |
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A) f (x)= log 1 |
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B) f (x)= log 1 (x+1) |
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C) f (x)= log 1 |
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D) f(x) = log2(x + 2) |
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E) f (x)= log 1(x – 2)
2
17.f(x) = 3x, (g f)(x) = 2x – 1 and g(p) = 3 are given. What is p?
A) |
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B) ñ3 |
C) 3 |
D) 9 |
E) 27 |
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18.How many digits does x have if log2(log3(log(5x))) = 1?
A) 5 |
B) 6 |
C) 8 |
D) 9 |
E) 10 |
19.What is x + y + z if log2(log3(log4 x)) = 0, log3(log4(log2 y)) = 0, and log4(log2(log3 z)) = 0?
A) 50 |
B) 58 |
C) 71 |
D) 89 |
E) 111 |
20. Calculate x2 + y2 given log2(x – y) = 5 – log2(x + y)
and |
log x – log 4 |
= –1. |
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log y – log 3 |
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A) 40 |
B) 48 |
C) 60 |
D) 74 |
E) 90 |
246 |
Algebra 11 |

CHAPTER REVIEW TEST 3F
1. Calculate log 0.09 if log 3 = 0.4771. |
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A) –2.9542 |
B) –1.9542 |
C) 0.0458 |
D) –2.4771 |
E) –1.0458 |
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2.log2 x = 98, log3 y = 56 and log5 z = 42 are given. Which statement is true?
A) z < y < x B) z < x < y C) y < z < x
D) y < x < z E) x < z < y
3.f(x) = 1 + ln x, g(x) = x2 and (f g)(a) = (g f )(a) are given. Find a.
A) |
1 |
B) ñe |
C) e |
D) e2 |
E) 1 |
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4. Calculate |
25log6 5 +49log 8 7 . |
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A) 7 |
B) 10 |
C) 12 |
D) 14 |
E) 28 |
5. Calculate log 25 using log 2 = 0.30103.
A) 0.48856 |
B) 0.69897 |
C) 1.29897 |
D) 1.39794 |
E) 1.42765 |
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6.What is the sum of the integers in the largest possible domain of f(x) = logx – 1(7 – x)?
A) 18 |
B) 20 |
C) 23 |
D) 24 |
E) 28 |
7.log 5 = x, log 3 = y and log 2 = z are given. Write log 1800 in terms of x, y and z.
A) x + 2y + 3z |
B) 2x + y + z |
C) x + 2y + z |
D) 3x + y + 2z |
E)2x + 2y + 3z
8.21(log x+ log y)= log[ 13( x+ y)] are given. What is (x – y)2?
A) 2xy B) 4xy C) 5xy D) 6xy E) 9xy
9. How many digits are there in 915 if log 3 0.477?
A) 12 |
B) 13 |
C) 14 |
D) 15 |
E) 16 |
10.How many natural numbers are there in the largest possible domain of f (x)= 4 ln(4 – x)?
A) 1 |
B) 2 |
C) 3 |
D) 4 |
E) 5 |
Chapter Review Test 3F |
247 |

11.f(x) = log3(x – 2) is given. Which figure shows the graph of f –1(x)?
A) |
y |
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B) |
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5 |
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3 |
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C) |
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E) y
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12.Given log7 13 = a and log13 17 = b, write log17 7 in terms of a and b.
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B) a + b |
C) a |
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D) a b |
E) b |
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a b |
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13. |
Evaluate log2 3 log3 |
4 log4 5 |
... log63 64. |
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D) 5 |
E) 6 |
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log3 29 =a, logb 29 = 2 and log43 |
c = 1 are given. |
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Which statement is true? |
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A) a < c < b |
B) b < c < a |
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D) c < a < b |
E) c < b < a |
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15.log3(a b) = 7 and log3 ab =1 are given. What is loga b?
A) 4 |
B) 3 |
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D) 1 |
E) |
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16. Evaluate 4log8 2 |
2 + log |
3 – |
2 |
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3 + 2). |
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E) 5 |
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17. If p(f(x)) = x |
f(x + 1), what is p(p(ln x))? |
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A) ln(x + 1) ln(x + 2) |
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B) x ln(x + 2) |
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C) (x + 1) ln(x + 2) |
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D) x ln(x + 2)x + 1 |
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E) (x + 2) ln(x + 1)x |
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18. Evaluate (b |
log100 a |
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log100 b |
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log a |
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log b |
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2 loga b ( a+b) |
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A) a |
B) b |
C) a + b |
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E) a b |
19.In the triangle ABC shown opposite, AD, BE and CF intersect at a point. Use the measurements in the figure to calculate x.
A
ex |
ln a |
FE
2 |
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B ln a2 D e-x C
A) 0 |
B) ln e |
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D) ln a E) |
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20. What is |
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(log 2) +(log 2) |
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A) 0 |
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B) log ñ2 |
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C) ñ2 log 2 |
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D) |
log( 1) |
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E) |
2 log( |
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2 |
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248 |
Algebra 11 |