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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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Knowledge Check

  • If log_(4)(x - 1) = log_(2)(x - 3) , then x may be

    A
    `x = 5`
    B
    `x = 9`
    C
    `x = 2`
    D
    `x = 4`

  • If log(x^(2) - 16) le log_(e) (4 x -11) , then

    A
    `4 lt x le 5 `
    B
    `x lt - 4 or x gt 4 `
    C
    `-1 le x le 5 `
    D
    `x lt -1 or x gt 5 `

  • If 3x + 4 (1 -x) gt 5x - 2 gt 4x -4, then the value of x is

    A
    2
    B
    `-2`
    C
    0
    D
    `-3`

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