A：$f\left(2^a\right)<f\left(2\right)<f\left({\log }_{2}a\right)$

B：$f\left(2\right)<f\left(2^a\right)<f\left({\log }_{2}a\right)$

C：$f\left({\log }_{2}a\right)<f\left(2^a\right)<f\left(2\right)$

D：$f\left(2\right)<f\left({\log }_{2}a\right)<f\left(2^a\right)$