Question

if log 2 = 0.3010 find the number of digits in 4^29

Answer 1

Please see the attachment

Answer 2

$Given \: log 2 = 0.3010 \: --(1)$

$Now , Find \: log \: 4^{29} \\= log \: (2^{2})^{29} \\= log \: 2^{2\times 29} \\= log \: 2^{58} \\= 58 log 2 \\= 58 \times 0.3010 \: [from \: (1) ]$

$= 17. 458$

$log \: 4^{29} = 17.458$

$\red { Number \:of \:digits \: in \: 4^{29}} \\= one \: more \: than \: characteristic \\ of \: log \: 4^{29}\\= 17 + 1 \\= 18$

Therefore.,

$\red { Number \:of \:digits \: in \: 4^{29}} \green {= 18}$

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