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

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


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

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

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

Solving for variable 'l'.

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

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

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

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

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

Combine like terms: 2lnx + 2lnx = 4lnx
1ln + 4lnx = -2lnx + 2lnx

Combine like terms: -2lnx + 2lnx = 0
1ln + 4lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(1 + 4x) = 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 + 4x)' equal to zero and attempt to solve:

Simplifying
1 + 4x = 0

Solving
1 + 4x = 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 + 4x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4x = 0 + -1
4x = 0 + -1

Combine like terms: 0 + -1 = -1
4x = -1

Add '-4x' to each side of the equation.
4x + -4x = -1 + -4x

Combine like terms: 4x + -4x = 0
0 = -1 + -4x

Simplifying
0 = -1 + -4x

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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