.5=(.85)^t

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.5=(.85)^t

Guest Feb 11, 2015

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$\\.5=(.85)^t\\\\ log(0.5)=log(0.85)^t\\\\ log(0.5)=t*log(0.85)\\\\ t=\frac{log(0.5)}{log(0.85)}\\\\$

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

Melody Feb 11, 2015

Melody · Answer 1 · 2015-02-11T10:39:18

$\\.5=(.85)^t\\\\ log(0.5)=log(0.85)^t\\\\ log(0.5)=t*log(0.85)\\\\ t=\frac{log(0.5)}{log(0.85)}\\\\$

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

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