Let $\displaystyle f(x) \in C[a,b] $ and let $\displaystyle f(x)>0 $ on $\displaystyle [a,b]$. Prove that

$\displaystyle exp(\frac{1}{b-a}\int_a^b \ln f(x) dx)\leq \frac{1}{b-a}\int_a^b f(x) dx$

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