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a2b3c4 \large a^2 b^3 c^4 a2b3c4
Let a,ba,ba,b and ccc be non-negative real numbers satisfying a+b+c=9a+b+c=9a+b+c=9. If the maximum value of the expression above can be expressed as 2x3y2^x 3^y2x3y, where xxx and yyy are integers, find log10xy\log_{10} x^y log10xy.
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