Ln(x-1)+Lnx^2=Ln(x^3-3x^2-8)

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Solution for Ln(x-1)+Lnx^2=Ln(x^3-3x^2-8) equation: 


Simplifying
Ln(x + -1) + Lnx2 = Ln(x3 + -3x2 + -8)

Reorder the terms:
nL(-1 + x) + Lnx2 = Ln(x3 + -3x2 + -8)
(-1 * nL + x * nL) + Lnx2 = Ln(x3 + -3x2 + -8)
(-1nL + nxL) + Lnx2 = Ln(x3 + -3x2 + -8)

Reorder the terms:
-1nL + nxL + nx2L = nL(-8 + -3x2 + x3)
-1nL + nxL + nx2L = (-8 * nL + -3x2 * nL + x3 * nL)
-1nL + nxL + nx2L = (-8nL + -3nx2L + nx3L)

Solving
-1nL + nxL + nx2L = -8nL + -3nx2L + nx3L

Solving for variable 'n'.

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

Add '8nL' to each side of the equation.
-1nL + nxL + 8nL + nx2L = -8nL + -3nx2L + 8nL + nx3L

Reorder the terms:
-1nL + 8nL + nxL + nx2L = -8nL + -3nx2L + 8nL + nx3L

Combine like terms: -1nL + 8nL = 7nL
7nL + nxL + nx2L = -8nL + -3nx2L + 8nL + nx3L

Reorder the terms:
7nL + nxL + nx2L = -8nL + 8nL + -3nx2L + nx3L

Combine like terms: -8nL + 8nL = 0
7nL + nxL + nx2L = 0 + -3nx2L + nx3L
7nL + nxL + nx2L = -3nx2L + nx3L

Add '3nx2L' to each side of the equation.
7nL + nxL + nx2L + 3nx2L = -3nx2L + 3nx2L + nx3L

Combine like terms: nx2L + 3nx2L = 4nx2L
7nL + nxL + 4nx2L = -3nx2L + 3nx2L + nx3L

Combine like terms: -3nx2L + 3nx2L = 0
7nL + nxL + 4nx2L = 0 + nx3L
7nL + nxL + 4nx2L = nx3L

Add '-1nx3L' to each side of the equation.
7nL + nxL + 4nx2L + -1nx3L = nx3L + -1nx3L

Combine like terms: nx3L + -1nx3L = 0
7nL + nxL + 4nx2L + -1nx3L = 0

Factor out the Greatest Common Factor (GCF), 'nL'.
nL(7 + x + 4x2 + -1x3) = 0


Subproblem 1
Set the factor 'nL' equal to zero and attempt to solve:

Simplifying
nL = 0

Solving
nL = 0

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

Simplifying
nL = 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 '(7 + x + 4x2 + -1x3)' equal to zero and attempt to solve:

Simplifying
7 + x + 4x2 + -1x3 = 0

Solving
7 + x + 4x2 + -1x3 = 0

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

Add '-7' to each side of the equation.
7 + x + 4x2 + -7 + -1x3 = 0 + -7

Reorder the terms:
7 + -7 + x + 4x2 + -1x3 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + x + 4x2 + -1x3 = 0 + -7
x + 4x2 + -1x3 = 0 + -7

Combine like terms: 0 + -7 = -7
x + 4x2 + -1x3 = -7

Add '-1x' to each side of the equation.
x + 4x2 + -1x + -1x3 = -7 + -1x

Reorder the terms:
x + -1x + 4x2 + -1x3 = -7 + -1x

Combine like terms: x + -1x = 0
0 + 4x2 + -1x3 = -7 + -1x
4x2 + -1x3 = -7 + -1x

Add '-4x2' to each side of the equation.
4x2 + -4x2 + -1x3 = -7 + -1x + -4x2

Combine like terms: 4x2 + -4x2 = 0
0 + -1x3 = -7 + -1x + -4x2
-1x3 = -7 + -1x + -4x2

Add 'x3' to each side of the equation.
-1x3 + x3 = -7 + -1x + -4x2 + x3

Combine like terms: -1x3 + x3 = 0
0 = -7 + -1x + -4x2 + x3

Simplifying
0 = -7 + -1x + -4x2 + 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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