$6 \cdot 32$ If $a=\log _{8} 225$, and $b=\log _{2} 15$, then expressing $a$ in terms of $b$ equals
(A) $\frac{b}{2}$.
(B) $\frac{2 b}{3}$.
(C) $b$.
(D) $\frac{3 b}{2}$.
(E) $2 b$.
(13th American High School Mathematics Examination, 1962)
[Solution] Given $8^{a}=225, 2^{b}=15$. That is, $2^{3 a}=15^{2}, 2^{2 b}=15^{2}$, thus $3 a=2 b$, or $a=\frac{2}{3} b$. Therefore, the answer is $(B)$.