If log 2 = 0.30103 and log 3 = 0.4771, find the number of digits in $(648)^{5}$
$log(648)^{5}$
= 5 log(648)
= 5 log(81 × 8)
= 5[log(81) + log(8)]
=$5 [log(3^{4}) + log(2^{3})] $
=5[4log(3) + 3log(2)]
= 5[4 × 0.4771 + 3 × 0.30103]
= 5(1.9084 + 0.90309)
= 5 × 2.81149
≈ 14.05
ie, $log(648)^{5}$ ≈ 14.05
ie, its characteristic = 14
Hence, number of digits in $(648)^{5}$ = 14+1 = 15
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