Math whiz help

[chuck.ells]

Is there a formula to work out the answer to “ how many doubles are needed to reach a certain amount”?
For instance, start with 50. double it = 100, double again =200 and so on. How many doubles, in this way to reach 200 million?

Thanks

 

[sim03]

50 x 2ⁿ = 200,000,000

2ⁿ = 4,000,000

n = ln 4,000,000 / ln 2 &asymp 15.20 / 0.69 &asymp 21.93 --> 22 doubles

Check: 50 x 2²² &asymp 209.7M > 200M

If a calculator isn't handy or doesn't have log function, just remember that 2¹⁰ = 1,024 &asymp 1,000. So for every 10 "doubles" simply add 3 zeros to your starting number. For example:

50 to start off
10 doubles --> ~50,000
20 doubles --> ~50,000,000
and so on.