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

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


Simplifying
ln(y + 1) + -1ln(y) = ln(x3) + -2ln(x + -1)

Reorder the terms:
ln(1 + y) + -1ln(y) = ln(x3) + -2ln(x + -1)
(1 * ln + y * ln) + -1ln(y) = ln(x3) + -2ln(x + -1)
(1ln + lny) + -1ln(y) = ln(x3) + -2ln(x + -1)

Multiply ln * y
1ln + lny + -1lny = ln(x3) + -2ln(x + -1)

Combine like terms: lny + -1lny = 0
1ln + 0 = ln(x3) + -2ln(x + -1)
1ln = ln(x3) + -2ln(x + -1)

Multiply ln * x3
1ln = lnx3 + -2ln(x + -1)

Reorder the terms:
1ln = lnx3 + -2ln(-1 + x)
1ln = lnx3 + (-1 * -2ln + x * -2ln)
1ln = lnx3 + (2ln + -2lnx)

Reorder the terms:
1ln = 2ln + -2lnx + lnx3

Solving
1ln = 2ln + -2lnx + lnx3

Solving for variable 'l'.

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

Add '-2ln' to each side of the equation.
1ln + -2ln = 2ln + -2lnx + -2ln + lnx3

Combine like terms: 1ln + -2ln = -1ln
-1ln = 2ln + -2lnx + -2ln + lnx3

Reorder the terms:
-1ln = 2ln + -2ln + -2lnx + lnx3

Combine like terms: 2ln + -2ln = 0
-1ln = 0 + -2lnx + lnx3
-1ln = -2lnx + lnx3

Add '2lnx' to each side of the equation.
-1ln + 2lnx = -2lnx + 2lnx + lnx3

Combine like terms: -2lnx + 2lnx = 0
-1ln + 2lnx = 0 + lnx3
-1ln + 2lnx = lnx3

Add '-1lnx3' to each side of the equation.
-1ln + 2lnx + -1lnx3 = lnx3 + -1lnx3

Combine like terms: lnx3 + -1lnx3 = 0
-1ln + 2lnx + -1lnx3 = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-1 + 2x + -1x3) = 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 + 2x + -1x3)' equal to zero and attempt to solve:

Simplifying
-1 + 2x + -1x3 = 0

Solving
-1 + 2x + -1x3 = 0

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

Add '1' to each side of the equation.
-1 + 2x + 1 + -1x3 = 0 + 1

Reorder the terms:
-1 + 1 + 2x + -1x3 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 2x + -1x3 = 0 + 1
2x + -1x3 = 0 + 1

Combine like terms: 0 + 1 = 1
2x + -1x3 = 1

Add '-2x' to each side of the equation.
2x + -2x + -1x3 = 1 + -2x

Combine like terms: 2x + -2x = 0
0 + -1x3 = 1 + -2x
-1x3 = 1 + -2x

Add 'x3' to each side of the equation.
-1x3 + x3 = 1 + -2x + x3

Combine like terms: -1x3 + x3 = 0
0 = 1 + -2x + x3

Simplifying
0 = 1 + -2x + x3

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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