Instead of

opendir dhandle,"log";
@dots = grep { /^log/ } readdir(dhandle);
for $item(@dots)
{
    @files=`ls -l $item`;
     print @files;
}
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you will want to use

my $dirname = "log";
opendir my $dir, $dirname
    or die "Couldn't read '$dirname' : $!";
my @files = map { "$dirname/$_" } readdir $dir;
[download]

Then you have the full filenames. Then you want to use the stat function to get the date and time of last modification of that file.

Then, you want to convert that to a string, by using POSIX::strftime(), and then you want to compare that to the date string that you check against.