ln(x^2-x)=ln(6)

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Solution for ln(x^2-x)=ln(6) equation:


Simplifying
ln(x2 + -1x) = ln(6)

Reorder the terms:
ln(-1x + x2) = ln(6)
(-1x * ln + x2 * ln) = ln(6)
(-1lnx + lnx2) = ln(6)

Reorder the terms for easier multiplication:
-1lnx + lnx2 = 6ln

Solving
-1lnx + lnx2 = 6ln

Solving for variable 'l'.

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

Add '-6ln' to each side of the equation.
-1lnx + -6ln + lnx2 = 6ln + -6ln

Reorder the terms:
-6ln + -1lnx + lnx2 = 6ln + -6ln

Combine like terms: 6ln + -6ln = 0
-6ln + -1lnx + lnx2 = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-6 + -1x + x2) = 0

Factor a trinomial.
ln((-2 + -1x)(3 + -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 '(-2 + -1x)' equal to zero and attempt to solve: Simplifying -2 + -1x = 0 Solving -2 + -1x = 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 + -1x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1x = 0 + 2 -1x = 0 + 2 Combine like terms: 0 + 2 = 2 -1x = 2 Add 'x' to each side of the equation. -1x + x = 2 + x Combine like terms: -1x + x = 0 0 = 2 + x Simplifying 0 = 2 + x 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 '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Add 'x' to each side of the equation. -1x + x = -3 + x Combine like terms: -1x + x = 0 0 = -3 + x Simplifying 0 = -3 + 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.

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