0.001=(1/8)^n n?

$$\\0.001=(1/8)^n\\\\ 0.001=8^{-n}\\\\ log(0.001)=log{8^{-n}}\\\\ -3=-nlog8\\\\ 3=nlog8\\\\ 3/log8=n\\\\$$

$${\frac{{\mathtt{3}}}{{log}_{10}\left({\mathtt{8}}\right)}} = {\mathtt{3.321\: \!928\: \!094\: \!887\: \!362\: \!7}}$$