Can Anyone help me with this problem, i need a formula to work out how long it takes Bacteria to multiply !

Ok heres the information i start out with:

Initial number of bacteria
End number of bacteria
Time elapsed

assumptions:
Bacteria grow by division into two, therefore each round of growth the number of bacteria double.
There are no deaths and the division is always perfect

So i want to know how long it takes for each division to complete.

eg start with 1 bacteria, end with 4 and total time is 4 hours, then the doubling time would be 2hours - 2 divisions / 4 hours
intuitive, easy ! but whats the formula ?

FYI the actual numbers involved would typically be

start 0.34
end 3.2x10^8
time 144 hours

Help !
TY