2. Given $a=\log _{8} 5, b=\log _{4} 3, c=\frac{2}{3}$. Then the size relationship of $a$, $b$, and $c$ is ( ).
(A) $a>b>c$
(B) $b>c>a$
(C) $b>a>c$
(D) $c>b>a$
2. C.

Notice,
$$
a=\log _{2} \sqrt[3]{5}>1, b=\log _{2} \sqrt{3}>1, c=\frac{2}{3}<1 \text {. }
$$

From $5^{2}<3^{3} \Rightarrow \sqrt[3]{5}<\sqrt{3}$. Therefore, $c<a<b$.