6.15 If $a^{x}=c^{q}=b$ and $c^{y}=a^{z}=d$, then
(A) $x y=q z$.
(B) $\frac{x}{y}=\frac{q}{z}$.
(C) $x+y=q+z$.
(D) $x-y=q-z$.
(E) $x^{y}=q^{z}$.
(2nd American High School Mathematics Examination, 1951)
［Solution］ From $c^{y}=a^{z}$, we have $c=a^{\frac{z}{y}}$. Therefore, $c^{q}=a^{\frac{z}{y} \cdot q}=a^{x}$, which gives $x=\frac{z q}{y}$, i.e., $x y=z q$. Hence, the correct choice is $(A)$.