262let logy x =z , therefore logx y = 1/z
z+1/z = 11
(z+1/z)2= 121
z2 + (1/z)2 = 119
sililarly we can find the rest
\hspace{-16}$Suppose that $\mathbf{\log_{y}x+\log_{x}y=11}$\\\\ Then Evaluate $\mathbf{(\log_{y}x)^k+(\log_{x}y)^k=}$\\\\ For $\mathbf{k=2\;,3\;,4\;,5}$
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