# 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 $$\log_{10} x^y$$.

×