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Simplifying ln(x + -6) = ln(x + 6) + -1ln(x + -4) Reorder the terms: ln(-6 + x) = ln(x + 6) + -1ln(x + -4) (-6 * ln + x * ln) = ln(x + 6) + -1ln(x + -4) (-6ln + lnx) = ln(x + 6) + -1ln(x + -4) Reorder the terms: -6ln + lnx = ln(6 + x) + -1ln(x + -4) -6ln + lnx = (6 * ln + x * ln) + -1ln(x + -4) -6ln + lnx = (6ln + lnx) + -1ln(x + -4) Reorder the terms: -6ln + lnx = 6ln + lnx + -1ln(-4 + x) -6ln + lnx = 6ln + lnx + (-4 * -1ln + x * -1ln) -6ln + lnx = 6ln + lnx + (4ln + -1lnx) Reorder the terms: -6ln + lnx = 6ln + 4ln + lnx + -1lnx Combine like terms: 6ln + 4ln = 10ln -6ln + lnx = 10ln + lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -6ln + lnx = 10ln + 0 -6ln + lnx = 10ln Solving -6ln + lnx = 10ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-10ln' to each side of the equation. -6ln + -10ln + lnx = 10ln + -10ln Combine like terms: -6ln + -10ln = -16ln -16ln + lnx = 10ln + -10ln Combine like terms: 10ln + -10ln = 0 -16ln + lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-16 + x) = 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 '(-16 + x)' equal to zero and attempt to solve: Simplifying -16 + x = 0 Solving -16 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + x = 0 + 16 Combine like terms: -16 + 16 = 0 0 + x = 0 + 16 x = 0 + 16 Combine like terms: 0 + 16 = 16 x = 16 Add '-1x' to each side of the equation. x + -1x = 16 + -1x Combine like terms: x + -1x = 0 0 = 16 + -1x Simplifying 0 = 16 + -1x 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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