log10 2 = 0.3010 the number of digits in 4^{2017} is …………….
log10 2 = 0.3010 the number of digits in 42017 is …………….
A) 2015
B) 2016
C) 1215
D) 1214
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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
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