Question

log₁₀ 2 = 0.3010 the number of digits in 4²⁰¹⁷ is ……………. 

A) 2015 

B) 2016 

C) 1215 

D) 1214

Answer 1

Correct option is (C) 1215

Let x \(=4^{2017}\)

Then \(log_{10}\,x=log_{10}\,4^{2017}\)   (By taking \(log_{10}\) both sides)

\(=2017\,log_{10}\,4\)

\(=2017\times2\,log_{10}\,2\)

= 4034 \(\times\) 0.3010

= 1214.234

\(\Rightarrow\) \(x=10^{1214.234}=10^{1214}\times10^{0.234}\)

\(=1.714\times10^{1214}\)

So total digits in \(4^{2017}\) = 1+1214 = 1215

Answer 2

Correct option is C) 1215