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Simplifying ln((x2) + -1) + -1ln(x + -1) = ln(6) ln(x2 + -1) + -1ln(x + -1) = ln(6) Reorder the terms: ln(-1 + x2) + -1ln(x + -1) = ln(6) (-1 * ln + x2 * ln) + -1ln(x + -1) = ln(6) (-1ln + lnx2) + -1ln(x + -1) = ln(6) Reorder the terms: -1ln + lnx2 + -1ln(-1 + x) = ln(6) -1ln + lnx2 + (-1 * -1ln + x * -1ln) = ln(6) -1ln + lnx2 + (1ln + -1lnx) = ln(6) Reorder the terms: -1ln + 1ln + -1lnx + lnx2 = ln(6) Combine like terms: -1ln + 1ln = 0 0 + -1lnx + lnx2 = 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)) = 0Subproblem 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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