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  4. If x= log 81 3, y= log 7 9 and z= log 9((√3/7)) then the value of (x y-y z) is equal to

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Q. If $x=\log _{81} 3, y=\log _7 9$ and $z=\log _9\left(\frac{\sqrt{3}}{7}\right)$ then the value of $(x y-y z)$ is equal to

Continuity and Differentiability

Solution:

$x =\frac{1}{4}, y =2 \log _7 3, z =\frac{1}{2}\left(\frac{1}{2}-\log _3 7\right)$
So, $\frac{1}{2} \log _7 3-\frac{1}{2} \log _7 3+1=1$.