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Simplifying ln(x + -2) + -1ln(x + 12) = ln(x + -1) * ln(x + 16) Reorder the terms: ln(-2 + x) + -1ln(x + 12) = ln(x + -1) * ln(x + 16) (-2 * ln + x * ln) + -1ln(x + 12) = ln(x + -1) * ln(x + 16) (-2ln + lnx) + -1ln(x + 12) = ln(x + -1) * ln(x + 16) Reorder the terms: -2ln + lnx + -1ln(12 + x) = ln(x + -1) * ln(x + 16) -2ln + lnx + (12 * -1ln + x * -1ln) = ln(x + -1) * ln(x + 16) -2ln + lnx + (-12ln + -1lnx) = ln(x + -1) * ln(x + 16) Reorder the terms: -2ln + -12ln + lnx + -1lnx = ln(x + -1) * ln(x + 16) Combine like terms: -2ln + -12ln = -14ln -14ln + lnx + -1lnx = ln(x + -1) * ln(x + 16) Combine like terms: lnx + -1lnx = 0 -14ln + 0 = ln(x + -1) * ln(x + 16) -14ln = ln(x + -1) * ln(x + 16) Reorder the terms: -14ln = ln(-1 + x) * ln(x + 16) Reorder the terms: -14ln = ln(-1 + x) * ln(16 + x) Reorder the terms for easier multiplication: -14ln = ln * ln(-1 + x)(16 + x) Multiply ln * ln -14ln = l2n2(-1 + x)(16 + x) Multiply (-1 + x) * (16 + x) -14ln = l2n2(-1(16 + x) + x(16 + x)) -14ln = l2n2((16 * -1 + x * -1) + x(16 + x)) -14ln = l2n2((-16 + -1x) + x(16 + x)) -14ln = l2n2(-16 + -1x + (16 * x + x * x)) -14ln = l2n2(-16 + -1x + (16x + x2)) Combine like terms: -1x + 16x = 15x -14ln = l2n2(-16 + 15x + x2) -14ln = (-16 * l2n2 + 15x * l2n2 + x2 * l2n2) -14ln = (-16l2n2 + 15l2n2x + l2n2x2) Solving -14ln = -16l2n2 + 15l2n2x + l2n2x2 Solving for variable 'l'. Reorder the terms: -14ln + 16l2n2 + -15l2n2x + -1l2n2x2 = -16l2n2 + 16l2n2 + 15l2n2x + -15l2n2x + l2n2x2 + -1l2n2x2 Combine like terms: -16l2n2 + 16l2n2 = 0 -14ln + 16l2n2 + -15l2n2x + -1l2n2x2 = 0 + 15l2n2x + -15l2n2x + l2n2x2 + -1l2n2x2 -14ln + 16l2n2 + -15l2n2x + -1l2n2x2 = 15l2n2x + -15l2n2x + l2n2x2 + -1l2n2x2 Combine like terms: 15l2n2x + -15l2n2x = 0 -14ln + 16l2n2 + -15l2n2x + -1l2n2x2 = 0 + l2n2x2 + -1l2n2x2 -14ln + 16l2n2 + -15l2n2x + -1l2n2x2 = l2n2x2 + -1l2n2x2 Combine like terms: l2n2x2 + -1l2n2x2 = 0 -14ln + 16l2n2 + -15l2n2x + -1l2n2x2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-14 + 16ln + -15lnx + -1lnx2) = 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 '(-14 + 16ln + -15lnx + -1lnx2)' equal to zero and attempt to solve: Simplifying -14 + 16ln + -15lnx + -1lnx2 = 0 Solving -14 + 16ln + -15lnx + -1lnx2 = 0 Move all terms containing l to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 16ln + -15lnx + 14 + -1lnx2 = 0 + 14 Reorder the terms: -14 + 14 + 16ln + -15lnx + -1lnx2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + 16ln + -15lnx + -1lnx2 = 0 + 14 16ln + -15lnx + -1lnx2 = 0 + 14 Combine like terms: 0 + 14 = 14 16ln + -15lnx + -1lnx2 = 14 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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