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
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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.
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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
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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.
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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
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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.
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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
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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.
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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
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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
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