line number of the current file handle is stored in the special variable $.

You may note that $. is reset only by an explicit close of the filehandle, so if the same filehandle is reopened $. continue grows between files. This can be avoided with close ARGV if eof that is very useful for oneliners.

perl -lne "print qq($.)" two_lines.log 13_lines.log
1
2
3  #<--here starts second file          
4
5
6
7
8
9
10
11
12
13
14
15

perl -lne "print qq($.); close ARGV if eof" two_lines.log 13_lines.log
1
2
1  #<--here starts second file
2
3
4
5
6
7
8
9
10
11
12
13
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