You haven’t told us what any of the constants are. So I created a simplified version which I believe is a special case of your objective function.
f := log(1+a)+log(1+a)/(log(1+a)-1)
The 2nd derivative of f can be of either sign, depending on the value of a. Choosing a = 15, the constraint is satisfied and the 2nd derivative of f is negative, so the objective function is not convex on the entirety of the feasible set you have shown us, let alone on the entirety of its natural domain.
If there are specific values of the constants such that this is a convex optimization problem, you need to tell us what they are, and show us your convexity proof. However, if the objective function is convex on the feasible set, but not for the entirety of its natural domain, the prospects for being able to enter it in CVX would not be good.