11 ALGEBRA

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 .
	x y yx
x x	x x	x	x	xy		yx
A) ( y)	B) ( y)	C) ( y)	D)	yx	E)
						xy

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 )			.
	(2	9x )+(4 9x 1) 32x
A) 5	B) 4	C) 3	D) 2		E) 1

2

5. Evaluate 2713 102.

162

A) 45

B) 75

C) 100

D) 225

E) 450

	6. Given	5a – 3a = k, evaluate			10a +6a			in terms
					50a – 18a
	of k.
	A) k2	B) k	C)	1	D)	1		E)	1
				k		k2			k3

7. Which statement is false?

A) 415	+ 415	= 231	B) 215 215 = 415
C) 215	+ 215	= 415	D) 2–15 > 0
		E) 415 215 = 245

8. Given 11443 = a, write		11888 +11886 – 122		in terms
of a.			11443 – 1
A) 122a	B) 122a2		C) 122(a – 1)
D) 122(a + 1)			E) a + 1

9. Evaluate		295 +294 +290 .
		292 +291 +287
A)	1	B) 1	C) 4	D) 8	E) 16
	8	4

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		0.05 105 +3000
			.
		0.005 104 0.01 103
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
	E) b < c < a

13. Evaluate	1			+	1		.
		7m 2	1			72 m 1
A) 1	B) 7m				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
	( ay )x y ( ax )x y.
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			y
graph shown opposite?	3
	1			x
	0		2	3
A) f(x) = 3x – 2	B) f(x) = 2x – 3
C) f(x) = 3x – 2	D) f(x) = 3x – 3
E) f(x) = 3x – 1

18.		3 26	32–32	= 8n	is given. Find n.
		32–29	128
	A) –3		B) 5		C) 7	D) –4	E) 6

19. Evaluate	( 5 – 1)	(1+	2	+ 3	5 ).
			5
					5
A) 3	B) 4	C) 5			D) 6	E) 7

20. Evaluate		3 128	– 3	16	.
		3 250	– 3	54
A)	2	B) 2			C) 1	D)	3	E)	5
	5	3					2		2

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)

3.What is the largest possible domain of f(x) = log4(2x + 1)?

A)	(–	1	, –	1)		B)	(–	1	, )			C)	(–	1	, )
		2		4				4						2
		D) (		1	, )				E)	(	1	, )
				2							4

4. Which function has the		y
graph shown opposite?		2		1	, 2)
				(16
A) f (x)= log 1 x		1
16					2
B) f (x)= log 1	x	0
			1	1		x
4		-1	16
		2			(2, -1 )
C) f (x)= log 1	x
					2
2

D)f(x) = log2 x

E)f(x) = log4 x

5. Calculate log2 32.
A) 1	B) 2	C) 4	D) 5	E) 6

6. Solve	log4 x=	1	for x.
		4
A) ñ2	B)	3 4	C) 4 2	D) 2	E) 6

7. logx 81 = –4 is given. What is x?

A)	1	B)	1	C)	1	D) 3	E) 9
	9		3		2

8. What is the logarithm of 125 to the base 5?

A) 5	B) 3	C) 2	D) 1	E)	1
					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, )			B) (0,	7	]	C) (0,	7 )
				5			5
D)	(	7	, )		E) (1,	7)
		5				5

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)	99
	2		2		2

13. Which graph shows y = ln x?

A)

y

B) y

1

0

e

x

0

1

e

x

C)

y

D) y

1

1

0

1

e

x

0

e

2e

x

E)y

1

0 1 e x

14. Given f(x) = ln x and (g f )(x) = x, find g(x).

	A) 10x B)	1	C)	x	D) ex E) ex + 1
		ex		ln x

15. Evaluate log 1000 – ln e2 – log4 64.
A) –3	B) –2	C) –1	D) 2	E) 3

16. log8 a =	4	is given. Find a.
	3
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)	–	1 ln3				B)	–	1 ln3		C)	1 ln3
		3						2			3
	D)		–	1	( ln3 – 1)			E)	1	( ln3 – 1)
				2					2

20. Evaluate	1	1		1
		–		+		.
	log12 6		log8 6		log 4 6
A) log6 3	B) log3 6			C) 0			D) 1	E) 2

242	Algebra 11

CHAPTER REVIEW TEST 3D

1. Evaluate log			2	2	23	2.
A)	6	B)		7		C)	8	D)	9	E)	8
	7			8			9		8		7

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
	a+ b		a+ b			a+1
	D) a – b – 1		E)	a+ b
				a+ b+1
	a+2

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)	1	B)	1	C)	1	D)	1	E)		1
		4		6		8		9		12

5. Which expression is equal to ln x + ln y – ln z?

A) ln(x + y – z)	B)	ln x+ y		C)	ln xy
			z		z
D) ln(xy – z)		E)	ln(x+ y)
			ln z

6. Evaluate log6 9		+ log6 12 + log62.
A) 3	B) 6	C) 9	D) 10	E) 12

7. Calculate 9a if a = log		3	5.
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	a		C) log		2a+ b
		a+2b			2				a+ b
	D) log(a – b)			E)		log	a2b
							a+2b

10. What is the common logarithm of				(0.4)2	?
				204
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		1		1		1
				+		–		.
		log24 30			log225 30		log 6 30
A)	1	B)	1		C) 1		D) 2		E) 3
	3		2

14. Evaluate (a4 )loga2 3 .
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?
		n			n
A)		1		B)	x		C)	x – 1
		x – 1			x+1			x
		D) –x – 1			E) x + 1

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)	5	B)	5	C)	4	D)	2	E)	3
	2		3		3		3		5

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?
A)	y			B)	y
	2				3
	1				2
	1		x		1	x
					1
C)	y			D)	y
	2				3
					2
	-1	2	x		1
					-1	x
			E)	y
				2
				1
			-3	-1	x
				-1
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	x
C) f –1(x) = log (x – 1)	D) f –1(x) = log (x + 1)
5	5

E) f –1(x) = –1 + log5 x

244	Algebra 11

CHAPTER REVIEW TEST 3E

1. If loga b = logb c = logc a, what is

5.

Given x = log

3, calculate

2

3x

– 2

–3x

.

loga c + logc a + logb a?

2

2x

– 2– x

A) 9

B) 4

C) 3

D) 2

E)

3

A)

11

B) 3

C) 5

1

D)

10 1

E)

10 1

2

2

9

9

7

9

2. Which function could have

y

the graph in the figure?

6.

log3 2 = a is given. What is log4 6?

A) f (x)= log 1(x – 3)

0

2a

a+1

a+1

3

-1

3

4

5 x

A)

B)

C)

B) f(x) = log3(x – 3)

a – 1

2a

a – 1

C) f (x)= log 1(x – 3)

D)

a – 1

E)

2a

2

2a

a+1

D)f(x) = log2(x – 3)

E)f (x)= –3+ log 1 x

3

7. In

the

triangle

ABC

A

3. p = log2 9, q = log3 83 and r = log5 123 are given.

shown opposite,

Which statement is true?

m( A) = (45 log6 y2)°,

A) p > r > q

B) q > p > r

C) r > q > p

m( B) = (90 log6 x)° and

D) r > p > q

E) q > r > p

m( C) = (180 log6 ñz)°.

B

C

If logx z y = –3, what is y?

4. Which figure shows the graph y = 1 + log2 x?

A) 36

B) 72

C) 144

D) 216

E) 256

A) y

B) y

2

3

2

1

8. Which statement is false?

1

< 0

0

21 1 2 x

A)

–1< log

B) 1 < log 11 < 2

0

1 1

2 x

2

9,9

C)	y			D)	y			C)	–3 < log	2	< –2	D) –3 < log 0.07 < –2
										201
	1				0	1	2	x		E) 3 < log 2		10	< 4
	0.5
	0	1	2	x	-1

E)y

			9. Evaluate	log	1003	0.0001 .
1					0.012
0	1 2 x		A) 7	B) 8		C) 9	D) 10	E) 12

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			B)	b		C)	b
	b				b – 1			b+1
	D)	b – 1			E)		1– b
		b+1					b

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
	3		2
	D) 2a + 3b		E)	b – 2a
				3

		3
14. Evaluate	2log9 2 .
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]		E) (2, 5]

16. Which function could		have
				y
the graph in the figure?					1
			-2 -3 -1		0 x
		2			-1
A) f (x)= log 1	(x+2)	B) f (x)= log 1 (x+1)
2				2
C) f (x)= log 1	(x – 1)	D) f(x) = log2(x + 2)
2

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)	1	B) ñ3	C) 3	D) 9	E) 27
	3

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.
	log y – log 3
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.
A) –2.9542	B) –1.9542	C) 0.0458
D) –2.4771	E) –1.0458

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
	e

		1		1
4. Calculate	25log6 5 +49log 8 7 .
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

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		B)	y
	5			5
	3			3
-1	0	x		0 1	x
C)	y		D)	y
				5
	3
	2			2
	0 1	x	-1	0	x

E) y

3

1

0 1 x

12.Given log7 13 = a and log13 17 = b, write log17 7 in terms of a and b.

	A)	1		B) a + b		C) a		D) a b	E) b
		a b
						b			a
13.	Evaluate log2 3 log3					4 log4 5	... log63 64.
	A) 2			B) 3		C) 4		D) 5	E) 6
14.	log3 29 =a, logb 29 = 2 and log43							c = 1 are given.
	Which statement is true?							2
	A) a < c < b				B) b < c < a			C) a < b < c
			D) c < a < b			E) c < b < a

15.log3(a b) = 7 and log3 ab =1 are given. What is loga b?

A) 4

B) 3

C)

2

D) 1

E)

1

3

4

3

3

4

16. Evaluate 4log8 2

2 + log

3 –

2

(

3 + 2).

A) 1

B) 2

C) 3

D) 4

E) 5

17. If p(f(x)) = x

f(x + 1), what is p(p(ln x))?

A) ln(x + 1) ln(x + 2)

B) x ln(x + 2)

C) (x + 1) ln(x + 2)

D) x ln(x + 2)x + 1

E) (x + 2) ln(x + 1)x

18. Evaluate (b

log100 a

log100 b

a

)

.

log a

log b

2 loga b ( a+b)

A) a

B) b

C) a + b

D) a – b

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	e
	e

B ln a2 D e-x C

A) 0	B) ln e			C)	ln 1			D) ln a E)		ln	1
					e						a
20. What is			2		1	2
		(log 2) +(log 2)					?
A) 0			B) log ñ2						C) ñ2 log 2
	D)	log( 1)			E)			2 log(	1)
		2							2

248	Algebra 11