INMO 2005 problem

Let α\alpha and β\beta be two positive integers such that 43197<αβ<1777\dfrac { 43 }{ 197 } <\dfrac { \alpha }{ \beta } <\dfrac { 17 }{ 77 } If the minimum possible value of β \beta is xx, find log2x\log _{ 2 }{ x } .

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