Is $a^{b}>b^{a}$ always true if $3\le a<b$ ?
My earlier question here made me wonder how the order of numbers affects the result when using exponents and when experimenting I noticed you usually get a higher number when raising a lower number to a higher exponent than vice versa. Now I'm wondering if the equation (is it still an equation despite not having an equal sign?) above is true or whether there are some numbers besides those less than three that make it false.
On a side note, are math novices welcome here in math.se? My first impression of it is intimidating and struggling to understand half the questions asked here makes me feel quite out of place! I do want to learn however and I like sharing these problems I come up with from time to time, but I'm not sure whether that's acceptable here or if the questions are supposed to be for more serious topics and for actual need of help. Apologies ahead of time for asking website related questions on the side, I couldn't ask any questions there before I get more reputation :)