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How can I prove that $E(\log f_\xi (\xi)) \geq E(\log f_\eta (\xi))$?

I can only say that by linearity and logarithm property $E(\log f_\xi(\xi)) - E(\log f_\eta(\xi)) = E(\log f_\xi(\xi) - \log f_\eta(\xi)) = E(\log\frac{f_\xi(\xi)}{f_\eta(\xi)})$. But why is it greater or equal to zero?

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    This is called Gibb's inequality. Article on Wikipedia has proof for it. – 2017-02-09
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    Thank you very much for fast and helpful answer. – 2017-02-09

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