The number  ${\log }_{2}3$  is 

 ${\log }_{2}3=\frac{m}{n},m,n\in N$
 $\Rightarrow 3=2^{m/n}\Rightarrow 3^n=2^m$
$\Rightarrow$ Odd number = even number, which is not valid
$\therefore {\log }_{2}7$  is not rational. It is irrational.