My first thought would be to use an XML parser (as previously suggested), but choroba has good point about XML format. Although it's not a one liner, I believe that the untested code below should do the trick.

use strict;

my $ip = '10.146.163.43';
my $logfile = "logfile.log";
my $log;

open(LOG,"<",$logfile) || die "Unable to open file '$logfile':  $!\n";
{
  local $/;
  $log = <LOG>; # slurping file into $log
}
close(LOG);

$log =~ m/(<request>.*?$ip.*?\/request>)/is;
print "Log for IP address $ip:\n\n$1\n";
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If you're on a *nix OS, you'll probably need to add the appropriate #! line at the top. I do most of my Perl stuff on Windows and haven't gotten in the habit of adding that line to my code.