A good way would be to use grep() to find if @directories contains $path.

print q[@directories has $path] if grep $_ eq $path, @directories;
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But if you want to do something each time you encounter $path in @directories you might want to use this approach

foreach (grep $_ eq $path, @directories) {
    # your code here
}
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If you're reading @directories from a file you'll probably want to remove the line endings with a chomp() otherwise $path won't match.
HTH

broquaint