Lolwut? Surely that depends both on the bear and where you hit with the axe. If you hit something vital, or damage the muscles/tendons too bad, it's not going to be coming after you anymore. One axe to the head = dead bear.
i think you might be underestimating the size and thickness of a bear
also i dont think bears get 'hurt' like people get hurt
i may be wrong or exaggerating slightly but i do know that one axe to the head will not stop a bear from killing you
it might die later if youre lucky? (lucky but dead)