ln(x^2+2x+1)=3ln(x+1)

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Solution for ln(x^2+2x+1)=3ln(x+1) equation:


Simplifying
ln(x2 + 2x + 1) = 3ln(x + 1)

Reorder the terms:
ln(1 + 2x + x2) = 3ln(x + 1)
(1 * ln + 2x * ln + x2 * ln) = 3ln(x + 1)
(1ln + 2lnx + lnx2) = 3ln(x + 1)

Reorder the terms:
1ln + 2lnx + lnx2 = 3ln(1 + x)
1ln + 2lnx + lnx2 = (1 * 3ln + x * 3ln)
1ln + 2lnx + lnx2 = (3ln + 3lnx)

Solving
1ln + 2lnx + lnx2 = 3ln + 3lnx

Solving for variable 'l'.

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

Add '-3ln' to each side of the equation.
1ln + 2lnx + -3ln + lnx2 = 3ln + -3ln + 3lnx

Reorder the terms:
1ln + -3ln + 2lnx + lnx2 = 3ln + -3ln + 3lnx

Combine like terms: 1ln + -3ln = -2ln
-2ln + 2lnx + lnx2 = 3ln + -3ln + 3lnx

Combine like terms: 3ln + -3ln = 0
-2ln + 2lnx + lnx2 = 0 + 3lnx
-2ln + 2lnx + lnx2 = 3lnx

Add '-3lnx' to each side of the equation.
-2ln + 2lnx + -3lnx + lnx2 = 3lnx + -3lnx

Combine like terms: 2lnx + -3lnx = -1lnx
-2ln + -1lnx + lnx2 = 3lnx + -3lnx

Combine like terms: 3lnx + -3lnx = 0
-2ln + -1lnx + lnx2 = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-2 + -1x + x2) = 0

Factor a trinomial.
ln((-1 + -1x)(2 + -1x)) = 0

Subproblem 1

Set the factor 'ln' equal to zero and attempt to solve: Simplifying ln = 0 Solving ln = 0 Move all terms containing l to the left, all other terms to the right. Simplifying ln = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Subproblem 2

Set the factor '(-1 + -1x)' equal to zero and attempt to solve: Simplifying -1 + -1x = 0 Solving -1 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -1x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1x = 0 + 1 -1x = 0 + 1 Combine like terms: 0 + 1 = 1 -1x = 1 Add 'x' to each side of the equation. -1x + x = 1 + x Combine like terms: -1x + x = 0 0 = 1 + x Simplifying 0 = 1 + x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Subproblem 3

Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Add 'x' to each side of the equation. -1x + x = -2 + x Combine like terms: -1x + x = 0 0 = -2 + x Simplifying 0 = -2 + x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.

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