Fitting Different Data Sets with different equations but same dependent variable

Hi,

I'm trying to simultaenously fit two equations to different data sets, where the two equations equal each other, and am looking for any recommendations on how to do this.

The first equation is y1 = x1/a+(x1/b)^c and the second equation is y2=ln((a-x2)/(a-b))/(-c)

I know that y1 = y2, and also at any point along the curve x1+x2 = x3, where I know the relation of x3 to y1, y2.

Is there any way or functions in Matlab I can use to solve this?

Thanks