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Simplifying ln(x + -6) + ln(x + -5) = ln(16 + -2x) Reorder the terms: ln(-6 + x) + ln(x + -5) = ln(16 + -2x) (-6 * ln + x * ln) + ln(x + -5) = ln(16 + -2x) (-6ln + lnx) + ln(x + -5) = ln(16 + -2x) Reorder the terms: -6ln + lnx + ln(-5 + x) = ln(16 + -2x) -6ln + lnx + (-5 * ln + x * ln) = ln(16 + -2x) -6ln + lnx + (-5ln + lnx) = ln(16 + -2x) Reorder the terms: -6ln + -5ln + lnx + lnx = ln(16 + -2x) Combine like terms: -6ln + -5ln = -11ln -11ln + lnx + lnx = ln(16 + -2x) Combine like terms: lnx + lnx = 2lnx -11ln + 2lnx = ln(16 + -2x) -11ln + 2lnx = (16 * ln + -2x * ln) -11ln + 2lnx = (16ln + -2lnx) Solving -11ln + 2lnx = 16ln + -2lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-16ln' to each side of the equation. -11ln + -16ln + 2lnx = 16ln + -16ln + -2lnx Combine like terms: -11ln + -16ln = -27ln -27ln + 2lnx = 16ln + -16ln + -2lnx Combine like terms: 16ln + -16ln = 0 -27ln + 2lnx = 0 + -2lnx -27ln + 2lnx = -2lnx Add '2lnx' to each side of the equation. -27ln + 2lnx + 2lnx = -2lnx + 2lnx Combine like terms: 2lnx + 2lnx = 4lnx -27ln + 4lnx = -2lnx + 2lnx Combine like terms: -2lnx + 2lnx = 0 -27ln + 4lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-27 + 4x) = 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 '(-27 + 4x)' equal to zero and attempt to solve: Simplifying -27 + 4x = 0 Solving -27 + 4x = 0 Move all terms containing l to the left, all other terms to the right. Add '27' to each side of the equation. -27 + 27 + 4x = 0 + 27 Combine like terms: -27 + 27 = 0 0 + 4x = 0 + 27 4x = 0 + 27 Combine like terms: 0 + 27 = 27 4x = 27 Add '-4x' to each side of the equation. 4x + -4x = 27 + -4x Combine like terms: 4x + -4x = 0 0 = 27 + -4x Simplifying 0 = 27 + -4x 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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