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MATHSBOOKS - CENGAGE MATHS (ENGLISH)

LOGARITHM AND ITS APPLICATIONS

SINGLE CORRECT ANSWER TYPE

1. if x ∈ N, then the value of x satisfying the equation

5x ⋅ 8x - 11

x = 500 is divisible by

A. 2

B. 4

C. 3

D. 5

( )

Answer: C

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2. If log1755x = log3437x, then the value of log42 x4 - 2x2 + 7 is

A. 1

B. 2

C. 3

D. 4

Answer: A

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( )

3. The value of log10 √3 - √5 + √3 + √5 is ( )

A. 1/2

B. 1/4

C. 3/2

D. 3/4

Answer: A

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4. Which of the following is not the solution of 161 / x

2x+3> 1 ?

A. ( - ∞, - 4)

B. (0,1)

C. (0, ∞)

D. none of these

Answer: C

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5. If log4A = log6B = log9(A + B) then the value of BA

is

A. √5 - 14

B. √5 + 1

4

C. √5 - 12

D. √5 + 1

2

Answer: D

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6. The value of log 9

4

1

2√36 -

1

2√36 -

1

2√36 -

1

2√3...∞ is

( √ √ √ )

A. -2

B. -1

C. -1 /2

D. none of these

Answer: C

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7. Solve the equation logx2 - 6x+8 log2x2 - 2x+8 x2 + 5x = 0

A. 3

B. 2

C. 1

D. 0

Answer: C

[ ( )]

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8. IF 10logp logq logrx =1 and logq logr logpx = 0.

The value of p is

A. rq / r

B. rq

C. 1

D. rr /q

Answer: A

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{ ( ) } { ( )}

9. The greatest integer less than or equal to the number

log2(15) × log1

62 × log3

16

is ( )

A. 4

B. 3

C. 2

D. 1

Answer: C

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10. Given that log23 = a, log35 = b, log72 = c, express the

logaithm of the number 63 to the base 140 in terms of a,b and c.

A. 2 + ac

2c + 1 + abc

B. 1 + 2ac

c + 2 + abc

C. 1 + 2ac

2c + 1 + abc

D. 2 + ac

c + 2 + abc

Answer: C

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11. If log2x

4=log2y

6=log2z

3k and x3y2z = 1, then k is equal to

A. -8

B. -4

C. 0

D. 4

Answer: A

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12. A line x=k intersects the graph of y = log4x and y = log4(x + 4)

. The distance between the points of intersection is 0.5, then the

value of k is

A. 1

B. 2

C. 3

D. 4

Answer: D

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13. let N =log3135

log153-

log35

log4053 , then N equals

A. 1

B. 2

C. 3

( ) ( )

D. 4

Answer: C

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14. 1

logab(abc)+

1logbc(abc)

+1

logca(abc) is equal to:

A. 1/2

B. 1

C. 2

D. 4

Answer: C

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15. logaN. logbN + logcN. logbN + logaN. logcNis equals to

A. logaN. logbN. logcN

logabcN

B. logabcN

logaN. logbN. logcN

C. logNabc

logNa. logNb. logNc

D. none of these

Answer: A

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16. There exist positive integers A, B and C with no common

factors greater than 1, such that 1, such that

Alog2005 + Blog2002 = C The sum A + B + C equals

A. 5

B. 6

C. 7

D. 8

Answer: B

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17. 2log618 ⋅ 3log63

A. 6

B. 9

C. 12

D. 18

Answer: A

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( ) ( )

18. If logab = 2, logbc = 2, and log3c = 3 + log3 a,then the value

of c/(ab)is ________.

A. 1

B. 3

C. 9

D. 27

Answer: B

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19. If log210 = P;loge10

loge7= q and (11)r = 10, then which one of

the following expressions is equivalent to log10154 ?

A. pqr

B. 1pqr

C. p + q + r

pqr

D. pq + qr + rp

pqr

Answer: D

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20. If 3 log37x= 7 log73

x, then the value of x will be

A. 12

B. 14

C. 13

D. 1

Answer: A

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( ( ) ) ( ( ) )

21. The value 45log4√2 3 -√6 - 6log8 √3 -√2 is

A. 3

B. 6

C. 9

D. 27

Answer: C

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( ) ( )

22. Compute the following

811

( log ) 59 + 33

( log ) √63

409

.

√72

( log ) 257 - (125) ( log ) 256

A. 0

B. 1

C. 2

( )

Subjective Type

D. 3

Answer: B

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23. The value of 6log1040 ⋅ 5log1036 is

A. 200

B. 216

C. 432

D. none of these

Answer: B

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1. Find the value of x satisfying the equations

log3 log2x + log1 / 3 log1 / 2y = 1 and xy2 = 9

Answer: x=729

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( ) ( )

2. Let a and b be real numbers greater than 1 for which there

exists a positive real number c, different from 1, such that

2 logac + logbc = 9logabc. Find the largest possible value of

logab.

Answer: 2

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( )

3. Solve :

log3x. log4x. log5x = log3x. log4x + log4x. log5 + log5x. log3x.

Answer: 60

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4. Solve : 32log4(x + 2)

2 + 3 = log4(4 - x)3 + log4(6 + x)3.

Answer: x = 2, 1 - √23

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5. The value of x satisfying 5logx - 3logx - 1 = 3logx+1 - 5logx - 1 ,

where the base of logarithm is 10

Answer: 100

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6. Solve: logaxloga(xyz) = 48; logayloga(xyz) = 12;

logazloga(xyz) = 84

SINGLE CORRECT ANSWER TYPE

Answer: x = a4, y = a, z = a7

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7. Solve : 4√|x - 3|x+1 =

3√|x - 3|x - 2.

Answer: x = 4, 2 ; x = 11

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8. Solve : logx216+ log2x64=3.

Answer: x = 2 - 1 / 3, 4

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1. The value of x for which the equation 5 ⋅ 3log3x - 21 - log2x - 3 = 0

A. 1

B. 2

C. 25

D. 7

Answer: A

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2. The sum of all the values of a satisfying the equation

log10a -1

log10(a - 1) 2= log10a + log102

A. 0

B. 1

| |

C. 2

D. none of these

Answer: C

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3. The number of real solution(s) of the equation

9log3 logex = logex - logex2 + 1 is equal to

A. 0

B. 1

C. 2

D. 3

Answer: B

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( ) ( )

4. The solution set of the equation xlogx ( 1 - x )2= 9 is

A. { - 2, 4}

B. {4}

C. {0, - 2, - 4}

D. none of these

Answer: B

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5. 98. The value of x satisfying the equation

√π logπ ( x ) . √π logπ2 ( x ) . √π .logπ4 ( x ) . √π logπ8 ( x ) ...∞ = 3

is equal to

A. √π

B. π

(( ) ) (( ) ) (( ) ) (( ) )

C. 3

D. 13

Answer: C

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6. If a > 1, x > 0 and 2loga ( 2x ) = 5loga ( 5x ) , then x is equal to

A. 110

B. 15

C. 12

D. 1

Answer: A

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7. If x1 and x2 are solution of the equation

log5 log64|x| + (25)x -

12

= 2x, then

A. x1 = 2x2

B. x1 + x2 = 0

C. x1 = 3x2

D. x1x2 = 64

Answer: B

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8. Solve log69 - log927 + log8x = log64x - log64..

A. 1/2

B. 1/4

C. 1/8

D. 1/16

Answer: C

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9. If log2 log2 log2x = 2, then the number of digits in x, is

log102 = 0.3010

A. 7

B. 6

C. 5

D. 4

Answer: C

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( ( ))( )

10. The number of integers satisfying the inequality

log√0.9log5 √x2 + 5 + x > 0 is

A. 6

B. 7

C. 8

D. 9

Answer: C

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( )

11. The smallest integral x satisfying the inequality `(1-

log_(4)x)/(1+log_(2)x)le (1)/(2)x is.

A. √2

B. 2

C. 3

D. 4

Answer: B

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12. The number of integral solutions of

log9(x + 1). log2(x + 1) - log9(x + 1) - log2(x + 1) + 1 < 0 is

A. 4

B. 5

C. 6

D. 7

Answer: C

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13. The number of integers satisfying log 1

x

2(x - 2)(x + 1)(x - 5)

≥ 1 is

A. 0

B. 1

C. 2

D. 3

Answer: A

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( )

14. If log1 / 2(4 - x) ≥ log1 / 22 - log1 / 2(x - 1),then x belongs to

A. (1,2]

B. [1,3]

C. [3,4)

D. [2,3]

Answer: A::C

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15. Find the solution of the inequality

2log 14(x + 5) >

94log 1

3√3(9) + log√x+5(2)

A. ( - 5, - 4)

B. ( - 3, - 1)

C. ( - 4, - 1)

D. ( - 5, - 2)

Answer: A::B

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16. If log3x - log3x2 ≤

32log 1 / 2√2 4, then x can belong to (a)

( - ∞, 1 /3) (b) (9, ∞) (c) (1,6) (d) ( - ∞, 0)

A. ( - ∞, 1 /3)

B. (9, ∞)

C. (1,6)

D. ( - ∞, 0)

Answer: A::B

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( ) ( )

17. Which of the following is/are true ?

A. number of digits in 812535 is 35

B. number of digits in 812535 is 36

C. number of zeroes after decimal before a significant figures

starts in 827

20 is 10

D. number of zeroes after decimal before a significant figure

starts in 827

20 is 11

Answer: B::C

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