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If $2 \log (x+1)-\log \left(x^{2}-1\right)=\log 2$, then $x=$
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$\log \left\{\frac{(x+1)^{2}}{x^{2}-1}\right\}=\log 2 \Rightarrow(x+1)^{2}=2\left(x^{2}-1\right) \Rightarrow x^{2}-2 x-3=0 \Rightarrow(x-3)(x+1)=0$
$x=3 ; x \neq-1$
$\log \left\{\frac{(x+1)^{2}}{x^{2}-1}\right\}=\log 2 \Rightarrow(x+1)^{2}=2\left(x^{2}-1\right) \Rightarrow x^{2}-2 x-3=0 \Rightarrow(x-3)(x+1)=0$
$x=3 ; x \neq-1$
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