Do you see that listed as being allowed in the gp rules Geometric programming mode — CVX Users' Guide? I don’t.
Your objective function is concave within your constraint region of 0 < x < 1; so maximization over that domain is inherently a non-convex optimization problem. Actually it is a concave programming problem with compact constraints; therefore, its global maximum occurs at an extreme of the constraints, i.e…, at 0 or 1, and it happens to be at 1.
Your objective function is concave for x > 3, but because it is not concave over the entirety of its natural domain, the prospects for formulating within DCP rules, even if the problem is constrained to x > 3, are not good.