Script1.pl
----------
#!/usr/local/bin/perl

$logFl = "xyz.log";
open (FIRSTFH, "> $logFl") || die "couldn't open file...$!\n";
print FIRSTFH "This is from first script\n";
system("script2.pl $logFl");
#print FIRSTFH "This is second print in first script\n";

Script2.pl
----------
#!/usr/local/bin/perl
$logFl2 = "xyz.log";
open (FIRSTFH, ">> $logFl2") || die "couldn't open file in script2...$!\n";
print FIRSTFH "This is from second script\n";