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

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

Text Solution

Verified by Experts

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)`
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