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If `5^x=(0. 5)^y=1000 , then 1/x-1/y=`

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If `5^x=(0. 5)^y=1000 , then 1/x-1/y=`
A. 1
B. `(1)/(2)`
C. `(1)/(3)`
D. `(1)/(4)`
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Correct Answer - C
We have,
`5^(x) = (0.5)^(y) = 1000`
`rArr x = "log"_(5) 1000 " and " y = "log"_(0.5) 1000`
`rArr (1)/(x)-(1)/(y) = "log"_(1000) 5 -"log"_(1000) 0.5`
`rArr (1)/(x)-(1)/(y) = "log"_(1000) ((5)/(0.5)) = "log"_(1000) 10 = "log"_(10^(3)) 10 = (1)/(3)`
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