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Prove that (2^((log)2 1/4x)-3^((log)(27...

Prove that `(2^((log)_2 1/4x)-3^((log)_(27)(x^2+1)^3)-2x) /(7^(4(log)_(49)x)-x-1)>0`

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`(2^(log2^(1//4)x)-3^(log_(27)(x^(2)+1)^(3))-2x)/(7^(4log_(49)x)-x-1)`
`=(2^(log_(2)x^(4))-3^(log_(3)(x^(2)+1))-2x)/(7^(log_(7)x^(2))-x-1)`
`(x^(2)-(x^(2)+2x+1))/(x^(2)-x-1)`
`=x^(2)+x+1`
`(x+(1)/(2))^(2)+(3)/(4)gt0,AAx inR`
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