logarithm and its applications maths
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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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