Question

If $x={\log }_{81}3,y={\log }_{7}9$ and $z={\log }_9\left(\frac{\sqrt{3}}{7}\right)$ then the value of $(xy-yz)$ is equal to

• A. 0
• B. 1
• C. 2
• D. None of these

Answer 1

Answer: (B)

$x=\frac{1}{4},y=2{\log }_{7}3,z=\frac{1}{2}\left(\frac{1}{2}-{\log }_{3}7\right)$
So, $\frac{1}{2}{\log }_{7}3-\frac{1}{2}{\log }_{7}3+1=1$.