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Problem: log(x)+log(1+x)=0 [ Calculator, Method and examples ]

Solution:
Your problem `->` log(x)+log(1+x)=0


`log(x)+log(1+x)=0`

Simplify LHS `=log(x)+log(1+x)`

`=log(x)+log(1+x)`

`=log(x xx (1+x))`

`=log(x+x^2)`

Now, `log(x+x^2)=0`

`=>log(x+x^2)=0`

`=>x+x^2=10^0`

`=>x+x^2=1`

`=>x+x^2-1=0`

Comparing the given equation with the standard quadratic equation `ax^2+bx+c=0,`

we get, `a=1,b=1,c=-1`

`x_(1,2)=(-b+-sqrt(Delta))/(2a)` and `Delta=b^2-4ac`

`Delta=b^2-4ac`

`:.Delta=1^2-4*1*-1`

`:.Delta=1+4`

`:.Delta=5`

`:.sqrt(Delta)=sqrt(5)`

`:.sqrt(Delta)=2.2361`

`x_1=(-b+sqrt(Delta))/(2a)`

`:.x_1=(-1+2.2361)/(2*1)`

`:.x_1=(1.2361)/2`

`:.x_1=0.618`

`x_2=(-b-sqrt(Delta))/(2a)`

`:.x_2=(-1-2.2361)/(2*1)`

`:.x_2=(-3.2361)/2`

`:.x_2=-1.618`








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