Logarithm Problems - Logarithm Questions and Answers for SSC and Bank exams

Logarithm questions and answers for Competitive exams:

25. If log 2 = 0.30103, the number of digits in 2⁶⁴ is:

(A) 10

(B) 15

(C) 20

(D) 25

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26. If log 2 = 0.30103, the number of digits in 5²⁰ is:

(A) 14

(B) 18

(C) 22

(D) 24

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Solution

Taking logarithm on both sides

⇒  logx = log5²⁰

⇒ logx = 20log 5

⇒ logx = 20(0.699) where log5 = 0.699

⇒ logx = 13.98

⇒ The characteristic of x is 13

⇒ The characteristic of5²⁰is 13

Therefore, the number of digits in 5²⁰ is 14.

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