# Top 100+ Logarithm Aptitude Questions and Answers - 1

Question: 1

If log_{32} x = 0.8, then x is equal to

(A) 10

(B) 12.80

(C) 16

(D) 25.6

Ans: C

log_{32}x = 0.8 ⇔ x = (32)^{0.8}
= (2^{5})^{4/5} = 2^{4} = 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 (2^{3} × 3^{2} × 5)

= log 2^{3} + log 3^{2} + log 5
= 3 log 2 + 2 log 3 + log 5.

Question: 3

(log_{5}3) × (log_{3} 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 log_{10}2 = 0.3010, then log_{2}10 is equal to

(A) 0.3010

(B) 0.6990

(C) $${699}/{301}$$

(D) $${1000}/{301}$$

Ans: D

log_{2}10 = $${1}/{ log_{10}}2$$
= $${1}/{0.3010}$$ = $${10000} / {3010}$$ = $${1000} / {301}$$.

Question: 5

If log 2 = 0.30103, the number of digits in 2^{64} is

(A) 17

(B) 18

(C) 19

(D) 20

Ans: D

log(2^{64}) = 64 × log 2 = (64 × 0.30103) = 19.26592.

Its characteristic is 19. Hence, the number of digits in 2^{64} is 20.

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