INMO 2005 problem

Number Theory Level 4

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