ln(x^3-4x)-ln(x+2)=2lnx

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Solution for ln(x^3-4x)-ln(x+2)=2lnx equation:


Simplifying
ln(x3 + -4x) + -1ln(x + 2) = 2lnx

Reorder the terms:
ln(-4x + x3) + -1ln(x + 2) = 2lnx
(-4x * ln + x3 * ln) + -1ln(x + 2) = 2lnx
(-4lnx + lnx3) + -1ln(x + 2) = 2lnx

Reorder the terms:
-4lnx + lnx3 + -1ln(2 + x) = 2lnx
-4lnx + lnx3 + (2 * -1ln + x * -1ln) = 2lnx
-4lnx + lnx3 + (-2ln + -1lnx) = 2lnx

Reorder the terms:
-2ln + -4lnx + -1lnx + lnx3 = 2lnx

Combine like terms: -4lnx + -1lnx = -5lnx
-2ln + -5lnx + lnx3 = 2lnx

Solving
-2ln + -5lnx + lnx3 = 2lnx

Solving for variable 'l'.

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

Add '-2lnx' to each side of the equation.
-2ln + -5lnx + -2lnx + lnx3 = 2lnx + -2lnx

Combine like terms: -5lnx + -2lnx = -7lnx
-2ln + -7lnx + lnx3 = 2lnx + -2lnx

Combine like terms: 2lnx + -2lnx = 0
-2ln + -7lnx + lnx3 = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-2 + -7x + x3) = 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 + -7x + x3)' equal to zero and attempt to solve: Simplifying -2 + -7x + x3 = 0 Solving -2 + -7x + x3 = 0 Move all terms containing l to the left, all other terms to the right. Add '2' to each side of the equation. -2 + -7x + 2 + x3 = 0 + 2 Reorder the terms: -2 + 2 + -7x + x3 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -7x + x3 = 0 + 2 -7x + x3 = 0 + 2 Combine like terms: 0 + 2 = 2 -7x + x3 = 2 Add '7x' to each side of the equation. -7x + 7x + x3 = 2 + 7x Combine like terms: -7x + 7x = 0 0 + x3 = 2 + 7x x3 = 2 + 7x Add '-1x3' to each side of the equation. x3 + -1x3 = 2 + 7x + -1x3 Combine like terms: x3 + -1x3 = 0 0 = 2 + 7x + -1x3 Simplifying 0 = 2 + 7x + -1x3 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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