Please read Writeup Formatting Tips - in particular, surrounding your code with <code> tags will make it dramatically more legible. In the future, you should also include your output and a better description of your problem - saying "but it does not work" is usually frowned upon since there are many ways a code can "not work".

In your code, note that the line $recent = (stat(_))[9]; is missing a sigil in front of $_ - you mean $recent = (stat($_))[9];. The big problem you are encountering is likely that you are not testing your file name in your plus_recent subroutine to see if the file is a log file - you are locating the most recent file in your entire directory tree (after the $_ fix).

Note also in your commented open line you should likely use or in place of || - see Operator Precedence and Associativity.

Update: Learned something new re: stat. Thanks Bloodnok.