How to write expression x / (ln(1+x)*log(1+x)*log(1+x))

Nonconvex
2

This changes from convex to concave at about 45.06. So it can’t be used in CVX.

Even if there were some other constraint, constraining it to be within a convex region, it would not be convex over the entirety of its natural domain, and therefore it would be very unlikely to be representable in CVX.