Use one of the date functions like to get the 8 digit date in consecutive number order, like 01082003, then check to see if this number is a file:
file_exists("01082003.log");
You could also store this number as a variable and use it like that. Or you don't even have to name it like this. You could also have other text with it, like this:
file_exists("thislog-".$datevariable.".log");