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Positive numbers `x , y\ and\ z` satisfy `x y z\ =\ 10^(81)` and `(log_(10)x)*(log_(10)y z)+(log_(10)y)*(log_(10)z)= 468`. Find the value of `(log_(10)x)^2+(log_(10)y)^2+(log_(10)z)^2.`

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