If $a$ and $b$ are non-negative integers and $c$ and $d$ are non-negative real numbers, for what values is the following inequality true?
$\log((a+b)!) - \log(a!b!) \ge(a+b) \log(c+d) - (a \log(c) + b\log(d))$
I know that $log((a+b)!) \ge log(a!b!)$ and $(a+b)log(c+d) \ge alog(c)+ b log(d)$.