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

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

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

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

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

Reorder the terms:
1ln + -2ln + lnx + lnx = ln(x2)

Combine like terms: 1ln + -2ln = -1ln
-1ln + lnx + lnx = ln(x2)

Combine like terms: lnx + lnx = 2lnx
-1ln + 2lnx = ln(x2)

Multiply ln * x2
-1ln + 2lnx = lnx2

Solving
-1ln + 2lnx = lnx2

Solving for variable 'l'.

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

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

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

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

Factor a trinomial.
ln((-1 + x)(1 + -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 + x)' equal to zero and attempt to solve:

Simplifying
-1 + x = 0

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

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

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

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

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

Simplifying
0 = 1 + -1x

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 '(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.

The solution to this equation could not be determined.