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Simplifying ln(x + -5) = ln(x + -6) + ln(16 + -2x) Reorder the terms: ln(-5 + x) = ln(x + -6) + ln(16 + -2x) (-5 * ln + x * ln) = ln(x + -6) + ln(16 + -2x) (-5ln + lnx) = ln(x + -6) + ln(16 + -2x) Reorder the terms: -5ln + lnx = ln(-6 + x) + ln(16 + -2x) -5ln + lnx = (-6 * ln + x * ln) + ln(16 + -2x) -5ln + lnx = (-6ln + lnx) + ln(16 + -2x) -5ln + lnx = -6ln + lnx + (16 * ln + -2x * ln) -5ln + lnx = -6ln + lnx + (16ln + -2lnx) Reorder the terms: -5ln + lnx = -6ln + 16ln + lnx + -2lnx Combine like terms: -6ln + 16ln = 10ln -5ln + lnx = 10ln + lnx + -2lnx Combine like terms: lnx + -2lnx = -1lnx -5ln + lnx = 10ln + -1lnx Solving -5ln + lnx = 10ln + -1lnx 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. -5ln + -10ln + lnx = 10ln + -10ln + -1lnx Combine like terms: -5ln + -10ln = -15ln -15ln + lnx = 10ln + -10ln + -1lnx Combine like terms: 10ln + -10ln = 0 -15ln + lnx = 0 + -1lnx -15ln + lnx = -1lnx Add 'lnx' to each side of the equation. -15ln + lnx + lnx = -1lnx + lnx Combine like terms: lnx + lnx = 2lnx -15ln + 2lnx = -1lnx + lnx Combine like terms: -1lnx + lnx = 0 -15ln + 2lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-15 + 2x) = 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 '(-15 + 2x)' equal to zero and attempt to solve: Simplifying -15 + 2x = 0 Solving -15 + 2x = 0 Move all terms containing l to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + 2x = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 2x = 0 + 15 2x = 0 + 15 Combine like terms: 0 + 15 = 15 2x = 15 Add '-2x' to each side of the equation. 2x + -2x = 15 + -2x Combine like terms: 2x + -2x = 0 0 = 15 + -2x Simplifying 0 = 15 + -2x 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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