# Minimizing An Outlandish Expression

Algebra Level 2

$\large x \ln x + y \ln y + z \ln z$

Let $$x,y$$ and $$z$$ be positive numbers satisfying $$x+y + z= 3e$$.

Find the minimum value of the expression above.

 Clarification: $$e \approx 2.71828$$ denotes the Euler's number.

###### Dedicated to Sharky Kesa.
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