## Need help of proving an inequality of intergrals

Let $f(x) \in C[a,b]$ and let $f(x)>0$ on $[a,b]$. Prove that
$exp(\frac{1}{b-a}\int_a^b \ln f(x) dx)\leq \frac{1}{b-a}\int_a^b f(x) dx$

I have tried theorems of inequality I have learnt but I still cant solve this problem. Would you help me please? Thank you.