+118723
$$\begin{array}{rll}
0.05^{1/n}&=&0.8609\\\\
log(0.05^{1/n})&=&log0.8609\\\\
(1/n)log(0.05)&=&log0.8609\\\\
n&=&\frac{log0.05}{log0.8609}
\end{array}$$
$${\frac{{log}_{10}\left({\mathtt{0.05}}\right)}{{log}_{10}\left({\mathtt{0.860\: \!9}}\right)}} = {\mathtt{20.001\: \!293\: \!705\: \!215\: \!387\: \!9}}$$
.+118723
$$\begin{array}{rll}
0.05^{1/n}&=&0.8609\\\\
log(0.05^{1/n})&=&log0.8609\\\\
(1/n)log(0.05)&=&log0.8609\\\\
n&=&\frac{log0.05}{log0.8609}
\end{array}$$
$${\frac{{log}_{10}\left({\mathtt{0.05}}\right)}{{log}_{10}\left({\mathtt{0.860\: \!9}}\right)}} = {\mathtt{20.001\: \!293\: \!705\: \!215\: \!387\: \!9}}$$
