Question

How to prove that In(1+y) + In(1+x) =A that can be written as xy+x+y=C which A and C are constants.

Answer 1

\[\ln(1+y)+\ln(1+x)=\ln[(1+y)(1+x)]=A \rightarrow (1+y)(1+x)=e^A\]\[(1+y)(1+x)=xy+x+y+1=e^A \rightarrow xy+x+y=e^A-1=C\]Then, the expression is correct if:\[C=e^A-1\]

Answer 2

@CarlosGP

Answer 3

Why there is +1 at xy+x+y+1?

Answer 4

(x+1)(y+1)=xy+x+y+1

Answer 5

Okay.Thanks CarlosGP.

Answer 6

you are welcome