A Brilliant way to kick off 2k15

Algebra Level 4

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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