like"what is the exact size of the maximum range that can be searched in five steps?to solve thiswe must create similar tablebut one that starts at the beginningwith range of oneand works up from there by multiplying the range by two each time table shows how this looks for the first ten steps table powers of two step ssame as log (rrange range expressed as power of ( for our original problem with range of we can see that six steps doesn' produce range quite big enough ( )while seven steps covers it handily ( thusthe seven steps that are shown for items in table are correctas are the steps for range of doubling the range each time creates series that' the same as raising two to poweras shown in the third column of table we can express this as formula if represents steps (the number of times you multiply by two--that isthe power to which two is raisedand represents the rangethen the equation is if you know sthe number of stepsthis tells you rthe range for exampleif is the range is or the opposite of raising two to power