EDIT: As a quick test to reassure yourself, iterate for . Clearly x>1 but you should note some limiting behaviour..
Without even looking at any numbers, I can logically see that must be true. Assuming any situation, , for any results in decay. Unless of course aswell, but that would work contrary to obtaining a maximum. For , , . For both variables being positive also results in .
Therefore the only answer that would allow for a base being raised an infinite amount of times to the same value would be when
I know this isn't rigorous, but god-damnit it's right.