This set of Aptitude Questions and Answers (MCQs) focuses on “Properties of Logarithm”.
1. What will be the value of log385?
a) 9.863
b) 7.527
c) 9.463
d) 8.321
View Answer
Explanation: Given,
log385
log 85 / log3
5 log 23 / log3
5 * 3 log 2 / log3
15 * 0.3010 / 0.4771
4.515 / 0.4771
9.463
2. What will be the value of integer z if (log2z)2 – log2z4 – 32 = 0?
a) 256
b) 64
c) 16
d) 1024
View Answer
Explanation: Given,
(log2z)2 – log2z4 – 32 = 0
➩ (log2z)2 – 4log2z – 32 = 0
Let log2z = a
➩ a2 – 4a – 32 = 0
➩ a2 – 8a + 4a – 32 = 0
➩ a(a – 8) + 4(a – 8) = 0
➩ (a – 8) (a + 4) = 0
➩ a = 8, – 4
➩ log2z = 8 or log2z = – 4
➩ z = 28 = 256 or z = 2-4 = 1 / 16
Since z is an integer therefore z = 256.
3. If (1 / 4) log2a + 4log2b = 2 + log648, then which of the following is true?
a) a16 = 64 / b3
b) b16 = 64 / a
c) a16 = 64 / b
d) b16 = 64 / a4
View Answer
Explanation: Given,
(1 / 4) log2a + 4log2b = 2 + log648
➩ (1 / 4) log2a + 4log2b = 2 – 1 / log864
➩ log2 (a1/4 * b4) = 2 – \(\frac {1}{2}\) = 3 / 2
➩ a1/4 * b4 = 23/2
➩ ab16 = 64
➩ b16 = 64 / a
4. What will be the value log (8)1/3 / log (4)2?
a) 1 / 4
b) 1 / 8
c) 1 / 3
d) 1 / 6
View Answer
Explanation: Given,
log (8)1/3 / log (4)2
➩ log (23)1/3 / log (22)2
➩ log (2)3*1/3 / log (2)4
➩ log (2)3/3 / log (2)4
➩ log (2) / log (2)4
➩ log (2) / 4 log (2)
➩ (1 / 4) (log (2) / log (2))
➩ 1 / 4
5. Which of the following statements is not correct?
a) log101 = 0
b) log1010 = 1
c) log (5 + 7 + 9) = log5 + log7 + log9
d) log (3 + 4) = log (3 * 4)
View Answer
Explanation: Considering option d,
➩ log (3 + 4) = log 7
➩ log (3 * 4) = log 12
As, log 7 is not equal to log 12 therefore log (3 + 4) = log (3 * 4) is incorrect.
6. What will be the value of log10 (1 / 500) if log105 = z?
a) z – 4
b) z3 / 5
c) z – 3 / z
d) –(z + 2)
View Answer
Explanation: Given,
log10 (1 / 500)
➩ log101 – log10500
➩ -log10 (5 * 100)
➩ -(log105 + log10100)
➩ -(log105 + log10102)
➩ -(log105 + 2 log1010)
➩ -(z + 2)
7. Which value of a would satisfy log5 + log (a + 5) = log (5a + 10) + 1?
a) –1.66
b) 2.76
c) –3.45
d) –1.92
View Answer
Explanation: Given,
log5 + log (a + 5) = log (5a + 10) + 1
➩ log (5(a + 5)) = log (5a + 10) + log10
➩ log (5(a + 5)) = log (10(5a + 10))
➩ 5(a + 5) = 10(5a + 10)
➩ 5a + 25 = 50a + 100
➩ -45 a = 75
➩ a = -(75 / 45)
➩ a = -1.66
8. What will be the number of digits in 345?
a) 28
b) 21
c) 22
d) 23
View Answer
Explanation: log (345)
➩ 45 * log 3
➩ 45 * 0.4771
➩ 21.4695
Thus, the characteristic is 21. Therefore, there will be 21 + 1 = 22 digits in 345.
9. What will be the value of p if log516, log5(3p – 4), log5(3p + 97 / 16) are in arithmetic progression?
a) 9
b) 4
c) 2
d) 3
View Answer
Explanation: Given,
log516, log5(3p – 4), log5(3p + 97 / 16) are in arithmetic progression.
➩ 2 log5 (3p – 4) = log516 + log5(3p + 97 / 16)
➩ log5 (3p – 4)2 = log5 [16(3p + 97 / 16)]
➩ (3p – 4)2 = 16(3p + 97 / 16)
Let 3p = q
➩ (q – 4)2 = 16(q + 97 / 16)
➩ q2 – 8q + 16 = 16q + 97
➩ q2 – 24q – 81 = 0
➩ q2 – 27q + 3q – 81 = 0
➩ q (q – 27) + 3(q – 27) = 0
➩ (q + 3) (q – 27) = 0
➩ q = -3, 27
As 3p is a positive number therefore, rejecting – 3.
Thus, 3p = 27
➩ 3p = 33 ⟹ p = 3
10. What will be the value of y if log2(log2(log3(log2y))) = 1?
a) 281
b) 332
c) 83
d) 36
View Answer
Explanation: Given,
log2(log2(log3(log2y))) = 1
➩ log2(log3(log2y)) = 21 = 2
➩ log3(log2y) = 22 = 4
➩ log2y = 34 = 81
➩ y = 281
To practice all aptitude questions, please visit “1000+ Quantitative Aptitude Questions”, “1000+ Logical Reasoning Questions”, and “Data Interpretation Questions”.
