Is God subject to logic?

Hello, I wanted to know the Rabbi's position on the question of whether God is subject to logic? (Or to avoid over-humanization, does logic have an objective dimension in reality?) For example, it is not possible to give free choice and prevent the problem of evil, knowledge and choice, etc.
For the answer is no, but it is impossible to understand this in our human mind. It is quite an evasion and can be given as a crushing answer to any question of faith, and this is, in my opinion, its weakness.
On the other hand, if the answer is yes, does that mean it is limited?
thanks.