Logarithm-7

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Find the number of digits in (i) 378 (ii) 5100

Solution: (i) Let x = 378

taking logarithm on both sides,

log x = log 378 = 78 log 3 = 78 (0.4771) = 37.2138

Since the characteristic is 37, the number of digits in x i.e. 378 is 38

(ii) Let x = 5100

taking logarithm on both sides

log x = log 5100 = 100 log 5 = 100 x 0.6989 = 69.89

Since the characteristic is 69, the number of digits in x i.e. 5100 is 70

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