Question

If $a^x=\sqrt{b},b^y=\sqrt[3]{3c}$ and $c^z=\sqrt{a}$ then the value of $xyz$ is

• A. $\frac{1}{2}$
• B. $\frac{1}{3}$
• C. $\frac{1}{6}$
• D. $\frac{1}{12}$

Answer 1

Answer: (D)

$\frac{1}{12}$

$a^x=\sqrt{b},b^y=\sqrt[3]{3c}and{c}^z=\sqrt{a}$
$a^{2x}=b,b^{3y}=c,c^{2z}=a$
Since, $b^{3y}=c$ $\Rightarrow$ $(a^{2x}{)}^{3y}=c\Rightarrow (a^{2z}{)}^{6xy}=a$
$a^{12xyz}=a$
$\Rightarrow xzy=\frac{1}{12}$
Hence, option 'D' is correct.