Me!
the population of a bacteria in a petri dish doubles every 12 hours. the population of the bacteria is initially 500 organisms.

how long will it take for the population of the bacteria to reach 800?

You want to know how long it'll take for the bacteria to grow
to (800/500) = 1.6 times their initial population.

The number of double-times it'll take is 

                         [ log(1.6) / (log(2) ]  =  0.6781 .

The double-time for these particular critters is 12 hours,
so it'll take them

                             0.6781  x  12 hours  =  8.137 hours

                                                                =  8 hours  8.2 minutes .