[tex]\log _2\left(x+2\right)-\log _2\left(x+1\right)=1 \\ \log _2\left(x+2\right)-\log _2\left(x+1\right)+\log _2\left(x+1\right)=1+\log _2\left(x+1\right) \\ \log _2\left(x+2\right)=1+\log _2\left(x+1\right) \\ \log _2\left(x+2\right)=\log _2\left(2\right)+\log _2\left(x+1\right) \\ \log _2\left(x+2\right)=\log _2\left(2\left(x+1\right)\right) \\ x+2=2\left(x+1\right) \\ x+2=2x+2 \\ x=2x=\ \textgreater \ x=0[/tex]
