my %fh; # key: path, value: filehandle

if ($cond1) {
    my $text = "text1\n";
    $text .= somefunc(); # whatever
    append($path1, $text);
} elsif ($cond2) {
    my $text = "some other text\n";
    append($path2, $text);
} elsif (...) {
    ...
} else {
    ...
}

# when done:
close $fh{$_} for keys %fh;

sub append {
    my ($path, $text) = @_;
    unless ( exists $fh{$path} ) {
        open my $fh, '>>', $path or die "Can't append to $path: $!\n";
        $fh{$path} = $fh;
    }
    print {$fh{$path}} $text;
}

##</code><code>##

my %paths = (
    LOG => '/path/to/log.txt',
    ERROR => '/path/to/errorlog.txt',
    INFO => '/path/to/info.txt',
);
my %fh; # key: token, value: filehandle

...
if (...) {
    $text = ...
    append('LOG',$text);
} else {
    ...
}

sub append {
   my ($token, $text) = @_;
   my$ fh
   unless (exists $fh{$token} ) {
       open my $fh, '>>', $paths{$token} or die $!;
       $fh{$token} = $fh;
   }
   print {$fh{$token}} $text;
}