The activity coefficient of component 1 in a binary solution is represented by

\[ \ln \gamma_{1}=a x_{2}^{2}+b x_{2}^{3}+c x_{2}^{4} \]

where \ (a, b\), and \(c\) are constants independent of concentrations. Obtain an expression for \(\gamma_{2}\) in terms of \(x_{1}\).