Logarithms Questions and Answers

This set of Aptitude Questions and Answers (MCQs) focuses on “Logarithms”. These questions are beneficial for various competitive exams, placement interviews, and entrance tests.

1. Given log103 = 0.477, what should be the value of log1090?
a) 0.954
b) 0.977
c) 1.954
d) 3.908
View Answer

Answer: c
Explanation: Given, log103 = 0.477.
log1081 = log10 (9 * 10)
= log109 + log1010
= log10(32) + 1
= 2log103 + 1
= (2 * 0.477) + 1
= 0.954 + 1
= 1.954

2. Let log105 = z, then what should be the value of log10(1/50)?
a) -(z + 1)
b) -(z2 + 2)
c) (z + 1)-1
d) (z + 1)/(z – 1)
View Answer

Answer: a
Explanation: Given,
log105 = z
log10 (1/50) = log101 – log1050
= -log10 (5 * 10)
= -(log105 + log1010)
= -(z + 1)

3. If xa = yb, then which of the following options is correct?
a) log y/log x = b/a
b) log x/log y = b/a
c) log x/log y = a/b
d) log a/log b = y/x
View Answer

Answer: b
Explanation: Given,
xa = yb
Then,
➩ log xa = log yb
➩ a log x = b log y
➩ log x/log y = b/a
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4. What should be the value of log10 (0.0000001)?
a) -7
b) 7
c) -1/7
d) -1
View Answer

Answer: a
Explanation: log10 (0.0000001) = log10 (1/10000000)
= log10 (1/107)
= log10 (10-7)
= -7 log1010
= -7 * 1
= -7

5. What could be the value of x, if log2[log2 (log4 x)] = 1?
a) 128
b) 512
c) 256
d) 1024
View Answer

Answer: c
Explanation: Given,
log3[log4 (log2 x)] = 1
➩ log2(log4 x) = 21 = 2
➩ log4 x = 22 = 4
➩ x = 44
➩ x = 256

6. What could be the value of z to satisfy log1020 + log105 = z?
a) 10
b) 1/10
c) 1/2
d) 2
View Answer

Answer: d
Explanation: Given,
log1020 + log105 = z
Thus, z = log10 (20 * 5).
➩ z = log10 (100)
➩ z = log10 (10)2
➩ z = 2 log1010
➩ z = 2(1) = 2

7. Which of the following options can be equated to (log10√9)/(log109)?
a) 1/2
b) 1/3
c) 3
d) 1/9
View Answer

Answer: a
Explanation: (log10√9)/(log109) = [log10 (9)1/2]/[log10 9]
= \((\frac {1}{2})\) (log10 9)/(log10 9)
= 1/2
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8. What should be the simplified value of log2√3 (1/12)?
a) 3
b) – 4
c) 2
d) – 2
View Answer

Answer: d
Explanation: log2√3 (1/12) = log2√3 (1/(2√3)2)
= log2√3/((2√3)-2)
= -2(log2√3 2√3)
= -2

9. If log1000X = -1/3, then which value of X from the options given below would satisfy this equation?
a) 10
b) 1/10
c) -1/10
d) -1/100
View Answer

Answer: b
Explanation: Given,
log1000X = -1/3
➩ X = (1000)-1/3
➩ X = (103)-1/3
➩ X = 10-1
➩ X = 1/10
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10. What would be the value of x, if log10(x – 10) = 1?
a) 20
b) 10
c) 100
d) 90
View Answer

Answer: a
Explanation: Given,
log10(x – 10) = 1
log10(x – 10) = log1010
➩ x – 10 = 10
➩ x = 10 + 10
➩ x = 20

More Aptitude Questions and Answers on Logarithms:

To practice all aptitude questions, please visit “1000+ Quantitative Aptitude Questions”, “1000+ Logical Reasoning Questions”, and “Data Interpretation Questions”.

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Manish Bhojasia - Founder & CTO at Sanfoundry
Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He lives in Bangalore, and focuses on development of Linux Kernel, SAN Technologies, Advanced C, Data Structures & Alogrithms. Stay connected with him at LinkedIn.

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