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 log_{10}3 = 0.477, what should be the value of log_{10}90?

a) 0.954

b) 0.977

c) 1.954

d) 3.908

View Answer

Explanation: Given, log

_{10}3 = 0.477.

log

_{10}81 = log

_{10}(9 * 10)

= log

_{10}9 + log

_{10}10

= log

_{10}(3

^{2}) + 1

= 2log

_{10}3 + 1

= (2 * 0.477) + 1

= 0.954 + 1

= 1.954

2. Let log_{10}5 = z, then what should be the value of log_{10}(1/50)?

a) -(z + 1)

b) -(z^{2} + 2)

c) (z + 1)^{-1}

d) (z + 1)/(z – 1)

View Answer

Explanation: Given,

log

_{10}5 = z

log

_{10}(1/50) = log

_{10}1 – log

_{10}50

= -log

_{10}(5 * 10)

= -(log

_{10}5 + log

_{10}10)

= -(z + 1)

3. If x^{a} = y^{b}, 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

Explanation: Given,

x

^{a}= y

^{b}

Then,

➩ log x

^{a}= log y

^{b}

➩ a log x = b log y

➩ log x/log y = b/a

4. What should be the value of log_{10} (0.0000001)?

a) -7

b) 7

c) -1/7

d) -1

View Answer

Explanation: log

_{10}(0.0000001) = log

_{10}(1/10000000)

= log

_{10}(1/10

^{7})

= log

_{10}(10

^{-7})

= -7 log

_{10}10

= -7 * 1

= -7

5. What could be the value of x, if log_{2}[log_{2} (log_{4} x)] = 1?

a) 128

b) 512

c) 256

d) 1024

View Answer

Explanation: Given,

log

_{3}[log

_{4}(log

_{2}x)] = 1

➩ log

_{2}(log

_{4}x) = 2

^{1}= 2

➩ log

_{4}x = 2

^{2}= 4

➩ x = 4

^{4}

➩ x = 256

6. What could be the value of z to satisfy log_{10}20 + log_{10}5 = z?

a) 10

b) 1/10

c) 1/2

d) 2

View Answer

Explanation: Given,

log

_{10}20 + log

_{10}5 = z

Thus, z = log

_{10}(20 * 5).

➩ z = log

_{10}(100)

➩ z = log

_{10}(10)

^{2}

➩ z = 2 log

_{10}10

➩ z = 2(1) = 2

7. Which of the following options can be equated to (log_{10}√9)/(log_{10}9)?

a) 1/2

b) 1/3

c) 3

d) 1/9

View Answer

Explanation: (log

_{10}√9)/(log

_{10}9) = [log

_{10}(9)

^{1/2}]/[log

_{10}9]

= \((\frac {1}{2})\) (log

_{10}9)/(log

_{10}9)

= 1/2

8. What should be the simplified value of log_{2√3} (1/12)?

a) 3

b) – 4

c) 2

d) – 2

View Answer

Explanation: log

_{2√3}(1/12) = log

_{2√3}(1/(2√3)

^{2})

= log

_{2√3}/((2√3)

^{-2})

= -2(log

_{2√3}2√3)

= -2

9. If log_{1000}X = -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

Explanation: Given,

log

_{1000}X = -1/3

➩ X = (1000)

^{-1/3}

➩ X = (10

^{3})

^{-1/3}

➩ X = 10

^{-1}

➩ X = 1/10

10. What would be the value of x, if log_{10}(x – 10) = 1?

a) 20

b) 10

c) 100

d) 90

View Answer

Explanation: Given,

log

_{10}(x – 10) = 1

log

_{10}(x – 10) = log

_{10}10

➩ x – 10 = 10

➩ x = 10 + 10

➩ x = 20

**More Aptitude Questions and Answers on Logarithms:**

- Logarithms Questions (Set 2)
- Logarithms Questions (Set 3)
- Logarithms Questions (Set 4)
- Logarithms Questions (Set 5)
- Logarithms Questions (Set 6)
- Logarithms Questions (Set 7)
- Logarithms Questions (Set 8)
- Logarithms Questions (Set 9)
- Logarithms Questions (Set 10)

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