.000061=.5^x

To find x take logs of both sides:

ln(0.000061) = ln(0.5^x)

 

Using the fact that ln(a^b) = b*ln(a) you have:

ln(0.000061)=x*ln(0.5)

 

or x = ln(0.000061)/ln(0.5)

$${\mathtt{x}} = {\frac{{ln}{\left({\mathtt{0.000\: \!061}}\right)}}{{ln}{\left({\mathtt{0.5}}\right)}}} \Rightarrow {\mathtt{x}} = {\mathtt{14.000\: \!831\: \!231\: \!761\: \!287\: \!9}}$$

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