Prove inequality $x^sy^{1-s} \leq sx + (1-s)y$ Given $s \in (0,1)$, prove $$x^sy^{1-s} \leq sx + (1-s)y$$ for $x,y > 0$
Tried some algebraic manipulations but I'm guessing I need to use some trick. 
Any suggestions, hints?

Hint :
$$\ln(x^sy^{1-s})=s\ln(x)+(1-s)\ln(y)\underset{why\ ?}{\leq} \ln(sx+(1-s)y)$$
