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If log3 = 0.4771 , find the number zeroes after the decimal in 3^(-100)

If log3 = 0.4771 , find the number zeroes after the decimal in 3^(-100)

Grade:9

2 Answers

Dhruv Sood
13 Points
7 years ago
Hi Let log x=3^(-100)Therefore log x=-100log3Taking the value of log 3 as 0.4771Log x =-100*0.4771X =-477.1X=bar(-478.21)Now number of zeroes=|-478+1|=477So 477 is the answer.
DR STRANGE
212 Points
7 years ago
hi,
let y = 3^(-100)
logy= -100log3 =-100*0.4771 = -47.71
=> y = 10^(-47)*10^(-0.71) where 10^(-0.71) > 10^(-1) =0.1
hence it has 47 zeros after decimal 

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