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

Prove that `(2^(log_(2^(1//4))x)-3^(log_(27)(x^(2)+1)^(3))-2x)/(7^(4log_(49)x)-x-1)gt0,AAx in(0,oo)`.

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To prove that the expression \[ \frac{2^{\log_{2^{1/4}} x} - 3^{\log_{27} (x^2 + 1)^3} - 2x}{7^{4 \log_{49} x} - x - 1} > 0 \quad \text{for } x \in (0, \infty), \] we will simplify the expression step by step. ...
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