The difference of roots of the equation ${\left({\log }_{27}{\mathrm{x}}^3\right)}^2={\log }_{27}{\mathrm{x}}^6$ is

$\begin{array}{l}{\left({\log }_{27}{\mathrm{x}}^3\right)}^2={\log }_{27}{\mathrm{x}}^6\\ \text{ or }{\left(3{\log }_{27}\mathrm{x}\right)}^2=6{\log }_{27}\mathrm{x}\\ \text{ or }3{\log }_{27}\mathrm{x}\left(3{\log }_{27}\mathrm{x}-2\right)=0\\ \Rightarrow \mathrm{x}=1\text{ or }{\log }_{27}\mathrm{x}=\frac{2}{3}\\ \Rightarrow \mathrm{x}=(27{)}^{2/3}=9\end{array}$

Difference=9-1 = 8