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

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


Simplifying
ln(x + -3) = ln(2x2 + -4) + -1lnx

Reorder the terms:
ln(-3 + x) = ln(2x2 + -4) + -1lnx
(-3 * ln + x * ln) = ln(2x2 + -4) + -1lnx
(-3ln + lnx) = ln(2x2 + -4) + -1lnx

Reorder the terms:
-3ln + lnx = ln(-4 + 2x2) + -1lnx
-3ln + lnx = (-4 * ln + 2x2 * ln) + -1lnx
-3ln + lnx = (-4ln + 2lnx2) + -1lnx

Reorder the terms:
-3ln + lnx = -4ln + -1lnx + 2lnx2

Solving
-3ln + lnx = -4ln + -1lnx + 2lnx2

Solving for variable 'l'.

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

Add '4ln' to each side of the equation.
-3ln + 4ln + lnx = -4ln + -1lnx + 4ln + 2lnx2

Combine like terms: -3ln + 4ln = 1ln
1ln + lnx = -4ln + -1lnx + 4ln + 2lnx2

Reorder the terms:
1ln + lnx = -4ln + 4ln + -1lnx + 2lnx2

Combine like terms: -4ln + 4ln = 0
1ln + lnx = 0 + -1lnx + 2lnx2
1ln + lnx = -1lnx + 2lnx2

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

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

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

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

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

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(1 + 2x + -2x2) = 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 + 2x + -2x2)' equal to zero and attempt to solve: Simplifying 1 + 2x + -2x2 = 0 Solving 1 + 2x + -2x2 = 0 Move all terms containing l to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + 2x + -1 + -2x2 = 0 + -1 Reorder the terms: 1 + -1 + 2x + -2x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2x + -2x2 = 0 + -1 2x + -2x2 = 0 + -1 Combine like terms: 0 + -1 = -1 2x + -2x2 = -1 Add '-2x' to each side of the equation. 2x + -2x + -2x2 = -1 + -2x Combine like terms: 2x + -2x = 0 0 + -2x2 = -1 + -2x -2x2 = -1 + -2x Add '2x2' to each side of the equation. -2x2 + 2x2 = -1 + -2x + 2x2 Combine like terms: -2x2 + 2x2 = 0 0 = -1 + -2x + 2x2 Simplifying 0 = -1 + -2x + 2x2 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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