Question

Let $x=\ln x,y=2\ln y,z=3\ln z$. Then the value of $x^{1/x}\cdot y^{1/y}\cdot z^{1/z}$ is equal to

• A. $e^{5/6}$
• B. $e^6$
• C. $e^{11/6}$
• D. $e^{1/6}$

Answer 1

Answer: (C)

$x^{1/x}=e,y^{1/y}=e^{1/2},z^{1/z}=e^{1/3}$
$x^{1/x}\cdot y^{1/y}\cdot z^{1/z}=e^{1+1/2+1/3}=e^{11/6}$