If log 10 2 = 0.3010 and log 10 3 = 0.4771, then find sum of the number of digits in 6 15 and the number of zeros immediately after the decimal in 3 –100 .
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Sol. log 10 2 = 0.3010 . log 10 3 = 0.4771
let x = 6 15
log 10 x = 15 log 10 6 = 15(log 10 2 + log 10 3) = 15(0.3010 + 0.4771) = 11.6715
∴ characteristic of 6 15 is 11 ∴ number of digits in 6 15 is 12.
let x = 3 –100
log 10 x = –100 log 10 3 = – 47.71
∴ number of zeroes immediately after the decimal in 3 –100 is 47.
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