Find the number of digits in $4^{2013}$ , if $l o g_{10} 2 = 0.3010$ .

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Solution

$4^{2013} = 2^{4026}$ .
No. of digits $= [4026 l o g 2] + 1$
$= 4026 (0.3010) + 1$
$= 1211.8260 + 1$
$= 1211 + 1$
$= 1212$ .

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