Is $a^b$ larger than $b^a$ if $a<b$ and $a,b > 1$?
I tried this out for a few numbers and this seems to be the case. If this is true, could you show me a proof? I would be very interested. If this is not true, can you give me a counter example?
I tested this for some powers, and an example is: $4^7 > 7^4$ as $16384 > 2401$