use strict;
use warnings;

use Test::More;

my @good = (
    '* leading asterisk',
    'trailing asterisk *',
    'multiple *** asterisk'
);

my @bad = (
    'foo',
    '',
    '^'
);

my $re = qr/\*/;

plan tests => @good + @bad;

for my $str (@good) {
    like ($str, $re, "$str matched");
}
for my $str (@bad) {
    unlike ($str, $re, "$str not matched");
}
[download]

See How to ask better questions using Test::More and sample data for how to write tests like this and formulate your question to fully illustrate the problem.

I happened to come across an issue of finding a string in 'non-regular' log file.

Define "non-regular". Do you just mean the lines have different lengths?