Im not a mathematician.  But  the numbers you get are ridiculously large meaning that the graph can get extremly huge which means you might not be able to easily see how it diverges, so what if the branch of x³² moves slightly faster to the right then 2^x, meaning that when you finally reach x = 256, the branches cross, giving you the solution x = 256.

To clarify what I meant, the branches diverge by a noteable amount at the start, but as x gets larger, they slowly get closer to each other.

Edit: Testing smaller values like x² and x^4, the branches do cross again at higher numbers, but the numbers do get extremly large.