log 2 = .301, log 3 = .477, find the number of digits in $(108)^{10}$

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Solution

The correct option is A
21
$(108)^{10}$ = y
Taking log on both sides
log $(108)^{10}$ = log y
10 log (27*4) = log y
10 (3log 3 + 2log 2) = log y
10 (1.43+0.602) = log y
Log y = 10 (2.032) = 20.3
No of digits is 21

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