ln(x^2+x)+lne=ln(x+1)

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Solution for ln(x^2+x)+lne=ln(x+1) equation: 


Simplifying
ln(x2 + x) + lne = ln(x + 1)

Reorder the terms:
ln(x + x2) + lne = ln(x + 1)
(x * ln + x2 * ln) + lne = ln(x + 1)
(lnx + lnx2) + lne = ln(x + 1)

Reorder the terms:
eln + lnx + lnx2 = ln(x + 1)

Reorder the terms:
eln + lnx + lnx2 = ln(1 + x)
eln + lnx + lnx2 = (1 * ln + x * ln)
eln + lnx + lnx2 = (1ln + lnx)

Add '-1lnx' to each side of the equation.
eln + lnx + -1lnx + lnx2 = 1ln + lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
eln + 0 + lnx2 = 1ln + lnx + -1lnx
eln + lnx2 = 1ln + lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
eln + lnx2 = 1ln + 0
eln + lnx2 = 1ln

Solving
eln + lnx2 = 1ln

Solving for variable 'e'.

Move all terms containing e to the left, all other terms to the right.

Add '-1lnx2' to each side of the equation.
eln + lnx2 + -1lnx2 = 1ln + -1lnx2

Combine like terms: lnx2 + -1lnx2 = 0
eln + 0 = 1ln + -1lnx2
eln = 1ln + -1lnx2

Divide each side by 'ln'.
e = 1 + -1x2

Simplifying
e = 1 + -1x2

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