Top 100+ Logarithm Aptitude Questions and Answers - 1
Question: 1
If log32 x = 0.8, then x is equal to
(A) 10
(B) 12.80
(C) 16
(D) 25.6
Ans: C
log32x = 0.8 ⇔ x = (32)0.8 = (25)4/5 = 24 = 16.
Question: 2
log 360 is equal to
(A) 2 log 2 + 3 log 3
(B) 3 log 2 + 2 log 3
(C) 3 log 2 + 2 log 3 + log 5
(D) 3 log 2 + 2 log 3 – log 5
Ans: C
360 = (2 × 2 × 2) × (3 × 3) × 5.
So, log 360 = log (23 × 32 × 5)
= log 23 + log 32 + log 5 = 3 log 2 + 2 log 3 + log 5.
Question: 3
(log53) × (log3 625) equals
(A) 2
(B) 3
(C) 4
(D) 5
Ans: C
Given expression
= $$({log 3} / {log 5} × {log 625} / {log 3})$$
= $${log 625}/{log 5}$$
= $${log(5^4)} / {log 5}$$
= $${4 log 5} / {log 5}$$ = 4.
Question: 4
If log102 = 0.3010, then log210 is equal to
(A) 0.3010
(B) 0.6990
(C) $${699}/{301}$$
(D) $${1000}/{301}$$
Ans: D
log210 = $${1}/{ log10}2$$ = $${1}/{0.3010}$$ = $${10000} / {3010}$$ = $${1000} / {301}$$.
Question: 5
If log 2 = 0.30103, the number of digits in 264 is
(A) 17
(B) 18
(C) 19
(D) 20
Ans: D
log(264) = 64 × log 2 = (64 × 0.30103) = 19.26592.
Its characteristic is 19. Hence, the number of digits in 264 is 20.
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