Positive numbers \( \mathrm{x}, \mathrm{y} \) and \( \mathrm{z} \) satisfy \( \mathrm{xyz}=10^{8....

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Positive numbers \( \mathrm{x}, \mathrm{y} \) and \( \mathrm{z} \) satisfy \( \mathrm{xyz}=10^{81} \) and
\( \mathrm{P} \)
\[
\left(\log _{10} \mathrm{x}\right)\left(\log _{10} \mathrm{yz}\right)+\left(\log _{10} \mathrm{y}\right)\left(\log _{10} \mathrm{z}\right)=468 .
\]
W
If the value of \( \left(\log _{10} \mathrm{x}\right)^{2}+\left(\log _{10} \mathrm{y}\right)^{2}+\left(\log _{10} \mathrm{z}\right)^{2}= \) \( \mathrm{k} \) then the value of \( \mathrm{k}-5620 \) is


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