This set of Aptitude Questions and Answers (MCQs) focuses on “Logarithms – Set 2”.
1. What is the value of log33 + log332 + log333 + log334 + ………… + log33n?
a) 2n2
b) n
c) n(n + 1) / 2
d) n + 1 / 3
View Answer
Explanation: Given,
log33 + log332 + log333 + log334 + ………… + log33n
➩ log33 + 2 log33 + 3 log33 + 4 log33 + ………… + n log33
➩ 1 + 2 + 3 + 4 ……. + n
➩ n(n + 1) / 2
2. What will be the value of (1 / logc+ab) + (1 / logc-ab), provided a, b and c are the sides of a right – angled triangle, where c is the hypotenuse?
a) 2
b) 6
c) 8
d) 12
View Answer
Explanation: Given,
(1 / logc+ab) + (1 / logc-ab)
➩ logb(c + a) + logb(c – a)
➩ logb[(c + a) (c – a)]
➩ logb(c2 – a2)
➩ logbb2
➩ 2 logbb
➩ 2
3. What will be the number of digits in 4812?
a) 20
b) 21
c) 19
d) 23
View Answer
Explanation:
➩ log 4812 = 12 log 48
➩ 12 log (24 * 3)
➩ 12 (4 log2 + log 3)
➩ 12 (4 * 0.3010 + 0.4771)
➩ 12 (1.204 + 0.4771)
➩ 12 * 1.6811
➩ 20.173
As the characteristic is 20, so the number of digits will be = 20 + 1 = 21.
4. Which of the following values of z will satisfy log3 [log2 (z2 – 4z – 37)] = 1?
a) 9, -5
b) -9, 5
c) 8, -3
d) -5, 7
View Answer
Explanation: Given,
log3 [log2 (z2 – 4z – 37)] = 1
➩ log2 (z2 – 4z – 37) = 3
➩ (z2 – 4z – 37) = 8
➩ z2 – 4z – 37 – 8 = 0
➩ z2 – 4z – 45 = 0
➩ z2 – 9z + 5z – 45 = 0
➩ (z – 9) (z + 5) = 0
➩ z = 9, – 5
5. What will be the value of the expression log (14 / 9) – log (16 / 15) + log (24 / 35)?
a) 7
b) 3
c) 0
d) 5
View Answer
Explanation: Given,
log (14 / 9) – log (16 / 15) + log (24 / 35)
➩ log (((14 / 9) * (24 / 35)) / (16 / 15))
➩ log ((14 / 9) * (24 / 35) * (15 / 16))
➩ log 1
➩ 0
6. What will be the value of (1 / (logxyz + 1)) + (1 / (logyzx + 1)) + (1 / (logzxy + 1))?
a) 12
b) 10
c) 3
d) 1
View Answer
Explanation: Given,
(1 / (logxyz + 1)) + (1 / (logyzx + 1)) + (1 / (logzxy + 1))
➩ (1 / (logxyz + logxx)) + (1 / (logyzx + logyy)) + (1 / (logzxy + logzz))
➩ (1 / (logxxyz)) + (1 / (logyzxy)) + (1 / (logzxyz))
➩ logxyzx + logxyzy + logxyzz
➩ logxyz(xyz)
➩ 1
7. Which value of p will satisfy log p – 2log3 = – 3?
a) 0.009
b) 0.027
c) 0.004
d) 0.008
View Answer
Explanation: Given,
log p – 2log3 = -3
➩ log p – log32 = -3
➩ log (p / 32) = – 3
➩ p / 9 = 10-3
➩ p / 9 = 1 / 1000
➩ p = 9 / 1000 = 0.009
8. Which value of a would satisfy log2a + log4a2 + log8a3 = 4?
a) 16 / 25
b) 9 / 16
c) 16 / 9
d) 4 / 9
View Answer
Explanation: Given,
➩ log2a + log4a2 + log8a3 = 4
➩ log2a + log4a2 + log8a3 = 4
➩ log2a + (2 / 2) log2a + (3 / 3) log2a = 4
➩ 3 log2a = 4
➩ log2a = 4 / 3
➩ a = (4 / 3)2
➩ a = 16 / 9
9. If logarithm of a number is -2.138, what will be its characteristic and mantissa respectively?
a) -3, 0.862
b) -4, 0.138
c) 3, -0.862
d) 4, -0.138
View Answer
Explanation: Let log x = -2.138
Then, log x = -2.138
= -2 + (- 0.138)
= (- 2 – 1) + (1 – 0.138)
= -3 + 0.862
Thus, the characteristic would be -3 and mantissa would be 0.862.
10. What will be the number of digits in 2100?
a) 32
b) 29
c) 30
d) 31
View Answer
Explanation: Given,
log2100
⟹ 100 log2
⟹ 100 * 0.3010
⟹ 30.10
Thus, the characteristic is 30 i.e., number of digits will be 30 + 1 = 31.
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