AIME Logarithm problem!

Level pending

Suppose that \(a,b,c\) are real positive integers such that,\[ a^{\log_{3}7}=27,b^{\log_{7}11}=49,c^{\log_{11}25}=\sqrt{11}\].Find the value of,\[ a^{(\log_{3}7)^{2}}+b^{(\log_{7}11)^2}+c^{(\log_{11}25)^2}\].

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