Should be able to do it in a single line ...

print  +(sort { $a->[1] <=> $b->[1] } map [$_, -M], <*.log>)[0]->[0];
[download]

There you're globbing on *.log, creating a list of anonymous arrays containing filename and timestamp, sorting on timestamp then getting the first element out of the sorted list and dereferencing the first element (which of course will contain the filename).
HTH

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broquaint