ln(1+y)-ln(y)=ln(x+1)-2ln(x-1)

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Solution for ln(1+y)-ln(y)=ln(x+1)-2ln(x-1) equation:


Simplifying
ln(1 + y) + -1ln(y) = ln(x + 1) + -2ln(x + -1)
(1 * ln + y * ln) + -1ln(y) = ln(x + 1) + -2ln(x + -1)
(1ln + lny) + -1ln(y) = ln(x + 1) + -2ln(x + -1)

Multiply ln * y
1ln + lny + -1lny = ln(x + 1) + -2ln(x + -1)

Combine like terms: lny + -1lny = 0
1ln + 0 = ln(x + 1) + -2ln(x + -1)
1ln = ln(x + 1) + -2ln(x + -1)

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

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

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

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

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

Solving
1ln = 3ln + -1lnx

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 + -3ln = 3ln + -3ln + -1lnx

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

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

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

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

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-2 + x) = 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 '(-2 + x)' equal to zero and attempt to solve: Simplifying -2 + x = 0 Solving -2 + x = 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 + x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + x = 0 + 2 x = 0 + 2 Combine like terms: 0 + 2 = 2 x = 2 Add '-1x' to each side of the equation. x + -1x = 2 + -1x Combine like terms: x + -1x = 0 0 = 2 + -1x Simplifying 0 = 2 + -1x 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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