I have a maximization problem in the form $$\max_{x} ~f(x)= \max_{x}~a ~\log(1+x) - b ~x \\ y ~x - c ~z ~ \log(1+x) \leq 0\\ a,b,c,x,y,z >0 $$
I computed the Hessian of the function $z ~ \log(1+x)$ and I found all the principal minors are negative. Can I use KKT conditions to solve or not?