🎴 Flashcard Mode

We have,

$ \log \left( -2x \right)=2\log \left( x+1 \right) $

$ \Rightarrow \log \left( -2x \right)=\log {{\left( x+1 \right)}^{2}} $

Comparing both side and we get,

$ -2x={{\left( x+1 \right)}^{2}} $

$ \Rightarrow -2x={{x}^{2}}+1+2x $

$ \Rightarrow {{x}^{2}}+4x+1=0 $

Using quadratic formula and we get,

$ x=\dfrac{-4\pm \sqrt{16-4\times 1\times 1}}{2\times 1} $

$ x=\dfrac{-4\pm \sqrt{12}}{2} $

$ x=\dfrac{-4\pm \sqrt{2\times 2\times 3}}{2} $

$ x=\dfrac{-4\pm 2\sqrt{3}}{2} $

$ x=-2\pm \sqrt{3} $

Hence,
this is the answer.