At what rate of interest does it take six years of compounding monthly for an account to double in value?
How do you get from,
(1+r/12)^72=2 to
r= 12(2^(1/72)-1)
i really don't get what you needed.. but if you are just solving for $\displaystyle r$ in $\displaystyle \left({\frac{1+r}{12}}\right)^{72} = 2$, then that is just simple algebra(and i think, there was a mistake in your grouping..)..
first, get the 72nd root of both sides, you will have $\displaystyle \frac{1+r}{12} = 2^{\frac{1}{72}}$
then multiply 12 to both sides, $\displaystyle 1+r = (12)(2^{\frac{1}{72}})$
lastly, subtract 1 to both sides, $\displaystyle r = (12)(2^{\frac{1}{72}}) - 1$
now, is that what you want?