If you're familiar with the basic 'single investment, compounding forward' set-up...

...whereis the amount the initial investment will grow to afterFperiods, the solution to your question starts with that basic layout:n

which immediately reduces to

Now solve for. Start by taking the logs of both sides, and remember that . Finally, remember that in this set-up,nrepresents the number ofnsemi-annualperiods it'll take for the investment to double...so youmightwanna re-express it as years in your final answer.