say every hour a bacteria splits into two, how long would it take for it to reach one million bacterias

We are looking for the answer to this....

2^N = 1,000,000   take the log of each side

log2^N  = log1,000,000    and by a property of logs, we have

N log2  = log1,000,000       and log of 1,000,000 = 6    so we have

N log 2  = 6                       divide both sides by log 2

N = 6/log2 = about 20 hrs