50 x 2<sup>n</sup> = 200,000,000
2<sup>n</sup> = 4,000,000
n = ln 4,000,000 / ln 2 &asymp 15.20 / 0.69 &asymp 21.93 --> 22 doubles
Check: 50 x 2<sup>22</sup> &asymp 209.7M > 200M
If a calculator isn't handy or doesn't have log function, just remember that 2<sup>10</sup> = 1,024...