\ln {\mu}_{12} = x_1 \cdot \ln {\mu}_1 +  x_2  \cdot \ln {\mu}_2 

\ln {\mu}_{12} = \frac{x_1}{x_1 + \alpha \, x_2} \cdot \ln {\mu}_1 +  \frac{\alpha \, x_2}{x_1 + \alpha \,x_2}  \cdot \ln {\mu}_2 

\ln {\mu}_{12} = x_1 \cdot \ln {\mu}_1 + x_2 \cdot \ln {\mu}_2 + \epsilon \, x_1 \, _2