Solved without a regex so it's even clearer

 if ( -1 != index $log, '198.167.1.10' ) {
     push @ip, $log;
# or...
     print $log
# or whatever makes sense for you
 }

# OR just written differently
 push @ip, $log if -1 != index $log, '198.167.1.10';
 print $log     if -1 != index $log, '198.167.1.10';

# Or... as a regexp but I prefer it the other way
 push @ip, $log if $log =~ /198\.167\.1\.10/;
 print $log     if $log =~ /198\.167\.1\.10/;
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Update Ok, maybe a regex is better because then then it can be written like /198\.167\.1\.10(?!\d)/ which would fix the problem Abigail-II pointed out.

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