Question 2
Suppose that $a,$ $b,$ and $c$ are positive real numbers such that $a^{\log_3 7} = 27,$ $b^{\log_7 11} = 49,$ and $c^{\log_{11} 25} = \sqrt{11}.$ Find $$
a^{(\log_3 7)^2} + b^{(\log_7 11)^2} + c^{(\log_{11} 25)^2}.
$$
a^{(\log_3 7)^2} + b^{(\log_7 11)^2} + c^{(\log_{11} 25)^2}.
$$