Logical Log... #1

Algebra Level 4

Suppose that a,b,cR+a, b, c \in \mathbb {R^{+}} , such that alog37=27a^{\log_3 7} = 27 , blog711=49b^{\log_7 11} = 49 , and clog1125=11c^{\log_{11}25} = \sqrt{11} . Find a(log37)2+b(log711)2+c(log1125)2.a^{(\log_3 7)^2} + b^{(\log_7 11)^2} + c^{(\log_{11} 25)^2}.

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