I'm not sure I've understood your question, but time will tell..

First of all I think you need some advice on syntax: in order of importance @arr & @arr2

perl -E "@a1=qw(1 2 3); @a2=qw(a b c d e); say for (@a1 & @a2)"

1

perl -E "@a1=qw(1 2 3); @a2=qw(a b c d e); say for (@a1 , @a2)"

1
2
3
a
b
c
d
e
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Infact to concatenate two list in list context the comma is used not & see perlop

Then your way to open filehandle, while running, is oldish and error prone:

open(FILE, "<x.log");
close (FILE);

# has to be

open my $file_handle, '<', 'x.log' or die "unable to open 'x.log' $!";
..
close $file_handle;
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Third, you are reassigning twice to @array2 = grep .. and, as long as you print to the destination file immediately, can also be what your intended, but is not clear and error prone in long distance: grep in list context will returns a list and you can use push to extend the array:

my @array;
...
#push 1

push @array, $_ for grep{..

#push 2

push @array, $_ for grep{..
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Also please use  <code> ..code tags.. </code> also for your data input/output

PS After reading twice, please clearify the following:

> Now I want to compare the data present after the keyword following colon(:) and in output file I have to print the mismatched lines from first data-set on comparing it with second data-set and number of lines in second data set that are not present in first data-set.

If I understand what you are asking for I'd go with a datastructure like a hash of arrays, which keys will be all keywords occurences and array element populed by the evntual presence in file 1 and file 2:

# pseudocode

my %report;

foreach my $line( $fh_one ){
 if... matching..
   extract the part interesting

   $report{  $interesting_part  }[0] = 1;  # first file populates the 
+element 0


foreach my $line( $fh_two ){
 if... matching..
   extract the part interesting

   $report{  $interesting_part  }[1] = 1;  # first file populates the 
+element 1 

   
# result like

%report = (

    interesting1 = [ undef, 1 ], # is present only in the second file
    interesting2 = [ 1, undef ], # is present only in the first file
    interesting3 = [ 1, 1 ],     # is present in both files
);
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L*