$$\\.5=(.85)^t\\\\
log(0.5)=log(0.85)^t\\\\
log(0.5)=t*log(0.85)\\\\
t=\frac{log(0.5)}{log(0.85)}\\\\$$
$${\frac{{log}_{10}\left({\mathtt{0.5}}\right)}{{log}_{10}\left({\mathtt{0.85}}\right)}} = {\mathtt{4.265\: \!024\: \!281\: \!798\: \!725\: \!7}}$$
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