# Logical Log... #1

Algebra Level 4

Suppose that $$a, b, c \in \mathbb {R^{+}}$$ , such that $$a^{\log_3 7} = 27$$ , $$b^{\log_7 11} = 49$$ , and $$c^{\log_{11}25} = \sqrt{11}$$ . Find $a^{(\log_3 7)^2} + b^{(\log_7 11)^2} + c^{(\log_{11} 25)^2}.$

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