Question 5Positive numbers $x,$ $y,$ and $z$ satisfy $xyz = 10^{81}$ and $(\log_{10} x)(\log_{10} yz)$ $+ (\log_{10} y)(\log_{10} z) = 468.$ Find $\small \sqrt{(\log_{10} x)^2 + (\log_{10} y)^2 + (\log_{10} z)^2}.$