Solve for \( x: \log ^{2}(4-x)+\log (4-x) \cdot \log \left(x+\frac{...

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Solve for \( x: \log ^{2}(4-x)+\log (4-x) \cdot \log \left(x+\frac{1}{2}\right)-2 \log ^{2}\left(x+\frac{1}{2}\right)=0 \)
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