Count number of cells that fall within a range of dates

I am creating a log that keeps track of how many of a certain product are sold within the month. The product is always sold one at a time, so i just need a formula that can will look at the date column and report how many entries fall within the given month. The date is entered in the following format: mm/dd/yy. I have tried using the COUNTIF function:

=COUNTIF(log!A2:log!A3000, CRITERIA)

However, I do not know how to set up the CRITERIA to calculate all dates within a month, since the dates are not entered just as month and year, but include the day.