Problem: If ax=cq=ba^{x}=c^{q}=bax=cq=b and cy=az=dc^{y}=a^{z}=dcy=az=d, then:
Answer Choices:
A. xy=qzx y=q zxy=qz
B. xy=qz\dfrac{x}{y}=\dfrac{q}{z}yx​=zq​
C. x+y=q+zx+y=q+zx+y=q+z
D. x−y=q−zx-y=q-zx−y=q−z
E. xy=qzx^{y}=q^{z}xy=qz Solution:
Since cy=az,c=az/y.∴cq=a(z/y)q=az;∴x=zq/y\quad c^{y}=a^{z}, \quad c=a^{z / y} . \quad \therefore c^{q}=a^{(z / y) q}=a^{z} ; \quad \therefore x=z q / ycy=az,c=az/y.∴cq=a(z/y)q=az;∴x=zq/y;
∴xy=qz.\therefore x y=q z . ∴xy=qz.