Problem

Which is larger epi or pie? How would you prove this?

Solution

Assume epi>pie
take logharitms pi ln e > e ln pi.
then pi/ln pi > e/ln e

is this true?

Conside the function y=x/ln x. Can we draw a graph?
It will have a turning point at dy/dx=0
ie ((1)*ln x - x(1/x))/(ln x)2 = 0
ie. When ln x=1 x=e.
This can be shown to be a minimum.
pi/ln pi > e/ln e proved.