In general, log(x/y) is neither convex nor concave. However, by virtue of the formula for a_m, there is a relation between the x and the y. This is sort of like log(x/(x+y)), which in general, is also neither convex nor concave. If this can be done, perhaps something similar to @Michal_Adamaszek 's technique in Can CVX solve this kind of function {x-log(1+0.01*x/(x+1))} can be used, although that problem only has a single variable, unlike the one you have presented.
Ir might help if you showed us the proof of concavity of the objective function. Is anything else being assumed than what is shown in the image?