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Find x if 9^(1//log(2)3) le log(2) x le ...

Find `x` if `9^(1//log_(2)3) le log_(2) x le log_(8) 27`

Text Solution

Verified by Experts

`9^(1//log_(2)3) = 9^(log_(3)2) = 3^(2 log_(3)2) = 3^(log_(3)4) = 4`
and `log_(8) 27 = log_((2^(3))(3^(3))) = (3)/(3)log_(2) 3 = log_(2)3`
Hence, by the given relation we may write that
`4 le log_(2) x le log_(2) 3 rArr 16 le x le 2^(log_(2)3)`
`rArr 16 le x le 3`
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