Just use the standard laundering technique (see perlsec): 
my $app_base = $ENV{AppBase};
if ($app_base =~ m{^(/var/www/[^/]+)$}) {
    $app_base = $1; # $app_base no longer tainted.
}
my $logfile = catdir($app_base, 'mylogfile');

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لսႽ† ᥲᥒ⚪⟊Ⴙᘓᖇ Ꮅᘓᖇ⎱ Ⴙᥲ𝇋ƙᘓᖇ

In reply to Re: How to safely define a CGI program's application base directory by choroba
in thread How to safely define a CGI program's application base directory by ddmiller

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