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If 4^(x + 1) - 16^(x) gt 2log(4)8 then x...

If `4^(x + 1) - 16^(x) gt 2log_(4)8` then `x` may be

A

`(1)/(2)`

B

`(3)/(2)`

C

`(3)/(4)`

D

`(4)/(3)`

Text Solution

Verified by Experts

The correct Answer is:
A, C
`4^(x) = y`
`4y - y^(2) gt 3`
`y^(2) - 4y + 3 lt 0`
`1 lt y lt 3`
`1 lt 4^(x) lt 3`
`0 lt x lt log_(4)3`
`log_(4)4 gt log_(4)3 gt log_(3)2sqrt(2) gt log_(4)3 gt log_(4)sqrt(2)`
`rArr 1 gt log_(4)3 gt (3)/(4) gt (1)/(2) gt (1)/(4)`
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