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

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


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

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

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

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

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

Combine like terms: 2lnx + lnx = 3lnx
3lnx = ln(2)

Reorder the terms for easier multiplication:
3lnx = 2ln

Solving
3lnx = 2ln

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.
-2ln + 3lnx = 2ln + -2ln

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

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-2 + 3x) = 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 + 3x)' equal to zero and attempt to solve:

Simplifying
-2 + 3x = 0

Solving
-2 + 3x = 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 + 3x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 3x = 0 + 2
3x = 0 + 2

Combine like terms: 0 + 2 = 2
3x = 2

Add '-3x' to each side of the equation.
3x + -3x = 2 + -3x

Combine like terms: 3x + -3x = 0
0 = 2 + -3x

Simplifying
0 = 2 + -3x

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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