A Brilliant way to kick off 2k15

Algebra Level 4

Consider the following equation:

log34log8(x2+7)+log12log14(x2+7)1=2.\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 xx which satisfy this equation are AA and A.-A. Then find A!A!

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