Solve `log(-x)=2log(x+1)dot`

Explanation

By definition, `xlt0andx+1lt0`.
`rArr-1ltxlt0`
`"Now "log(-x)=2log(x+1)`
`or-x=(x+1)^(2)`
`orx^(2)+3x+1=0`
`orx=(-3+sqrt(5))/(2),(-3-sqrt(5))/(2)`
Hence
`x=(-3+sqrt(5))/(2)` is the only solution. `(because(-3-sqrt(5))/(2)lt-1)`