Jetru wrote:I know that one(e^pi or pi^e).
e^pi can be written as e^pi*e/e
pi^e can be written as pi^e*pi/pi
Now thats in the form x^k/x.
Differentiate x^1/x and find maxima, which turns out to be at e.
So e^pi is greater.
That's a popular one.
Yeah, you seem to have seen it before, but you got the details wrong.
The function that has a maximum at e is log(x)/x. So
log(e)/e > log(pi)/pi
log(e)*pi > log(pi)*e
log(e^pi) > log(pi^e)
e^pi > pi^e