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s^(x)t^(1-x)<=xs + (1-x)t where s,t>=0 and 0<x<1.

Basically i've been asked to prove this. I've been fiddling about with it for a couple of hours

to no avail.

I've tried to substitute t=e^u and s=e^v and then use partial differentiation w.r.t to v on st, but i'm not getting the required form. (I can't assume that exp is a convex function - otherwise it follows trivially)

Thanks in advance.