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NDA 2018 Maths · Mathematics · Logarithms · medium

Given log 102=0.3010, how many digits does 2^20 have?

Single correct option

Given log⁡102=0.3010\log_{10}2=0.3010, how many digits does 2202^{20} have?
  1. A. 6
  2. B. 8
  3. C. 5
  4. D. 7
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Answer: (D) 7

log⁡10220=20×0.3010=6.02\log_{10}2^{20}=20\times0.3010=6.02. A number whose common logarithm has characteristic 6 has 6+1=76+1=7 digits (indeed 220=10485762^{20}=1048576). Reading the characteristic as the digit count gives 6.
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Original question written in the NDA 2018 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake