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Consider the following equation:

$\log_{\frac{3}{4}}\log_{8}(x^{2} + 7) + \log_{\frac{1}{2}}\log_{\frac{1}{4}}(x^{2} + 7)^{-1}= -2.$

The values of $x$ which satisfy this equation are $A$ and $-A.$ Then find $A!$

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