Find max value?

Algebra Level 4

a2b3c4 \large a^2 b^3 c^4

Let a,ba,b and cc be non-negative real numbers satisfying a+b+c=9a+b+c=9. If the maximum value of the expression above can be expressed as 2x3y2^x 3^y, where xx and yy are integers, find log10xy\log_{10} x^y .

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