If you're familiar with the basic 'single investment, compounding forward' set-up...
...where F is the amount the initial investment will grow to after n periods, the solution to your question starts with that basic layout:
which immediately reduces to
Now solve for n. Start by taking the logs of both sides, and remember that . Finally, remember that in this set-up, n represents the number of semi-annual periods it'll take for the investment to double...so you might wanna re-express it as years in your final answer.