This Article consist of most important ” Logarithm Questions and Answers ” that are mostly asked in all competitive exams. We collected these questions from the students who appeared in exams. Now try to solve these questions.

## Logarithm Questions and Answers

**Question : 1** If log 2 = 0.30103, the number of digits in 2^64 is:

A. 18

B. 19

C. 20

D. 21

**Show Answer**

**Correct Answer : ** **C**

**Explanation : **

log (2^64) = 64 x log 2

= (64 x 0.30103)

= 19.26592

Its characteristic is 19.

Hence, then number of digits in 2^64 is 20.

**Question : 2** If log10 5 + log10 (5x + 1) = log10 (x + 5) + 1, then x is equal to:

A. 1

B. 3

C. 5

D. 10

**Show Answer**

**Correct Answer : ** **B**

**Explanation : **

log10 5 + log10 (5x + 1) = log10 (x + 5) + 1

log10 5 + log10 (5x + 1) = log10 (x + 5) + log10 10

log10 [5 (5x + 1)] = log10 [10(x + 5)]

5(5x + 1) = 10(x + 5)

5x + 1 = 2x + 10

3x = 9

x = 3.

**Question : 3** If log10 2 = 0.3010, the value of log10 80 is:

A. 1.6020

B. 1.9030

C. 3.9030

D. None of these

**Show Answer**

**Correct Answer : ** **B**

**Explanation : **

log10 80 = log10 (8 x 10)

= log10 8 + log10 10

= log10 (2^3 ) + 1

= 3 log10 2 + 1

= (3 x 0.3010) + 1

= 1.9030.

**Question : 4 ** If log 27 = 1.431, then the value of log 9 is:

A. 0.934

B. 0.945

C. 0.954

D. 0.958

**Show Answer**

**Correct Answer : ** **C**

**Explanation : **

log 27 = 1.431

log (3^3 ) = 1.431

3 log 3 = 1.431

log 3 = 0.477

log 9 = log(3^2 ) = 2 log 3 = (2 x 0.477) = 0.954.

**Question : 5** If log 2 = 0.3010 and log 3 = 0.4771, the value of log5 512 is:

A. 2.870

B. 2.967

C. 3.876

D. 3.912

**Show Answer**

**Correct Answer : ** **C**

**Explanation : **

log5 512 = log 512/log 5

= log 29/log (10/2)

= 9 log 2/log 10 – log 2

= (9 x 0.3010)/1 – 0.3010

= 2.709/0.699

= 3.876