Find max value?

Algebra Level 4

$\large a^2 b^3 c^4$

Let $a,b$ and $c$ be non-negative real numbers satisfying $a+b+c=9$ . If the maximum value of the expression above can be expressed as $2^x 3^y$ , where $x$ and $y$ are integers, find $\log_{10} x^y$ .