$log(648)^{5}$

= 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