Is there a base $b$ such that:
$$\log_b x = x $$
(The only one that comes to mind would be the invalid case of $\log_1 1 = 1 $.)
I'm fairly certain the answer is no, but I can't find a clear justification for it.
(I don't have a strong mathematical background so an answer with the intuition would be much more helpful than any complex theorem proof.)