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Simplifying ln(x + -5) = -1ln(x + -1) + -1ln(x + 1) Reorder the terms: ln(-5 + x) = -1ln(x + -1) + -1ln(x + 1) (-5 * ln + x * ln) = -1ln(x + -1) + -1ln(x + 1) (-5ln + lnx) = -1ln(x + -1) + -1ln(x + 1) Reorder the terms: -5ln + lnx = -1ln(-1 + x) + -1ln(x + 1) -5ln + lnx = (-1 * -1ln + x * -1ln) + -1ln(x + 1) -5ln + lnx = (1ln + -1lnx) + -1ln(x + 1) Reorder the terms: -5ln + lnx = 1ln + -1lnx + -1ln(1 + x) -5ln + lnx = 1ln + -1lnx + (1 * -1ln + x * -1ln) -5ln + lnx = 1ln + -1lnx + (-1ln + -1lnx) Reorder the terms: -5ln + lnx = 1ln + -1ln + -1lnx + -1lnx Combine like terms: 1ln + -1ln = 0 -5ln + lnx = 0 + -1lnx + -1lnx -5ln + lnx = -1lnx + -1lnx Combine like terms: -1lnx + -1lnx = -2lnx -5ln + lnx = -2lnx Solving -5ln + lnx = -2lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '2lnx' to each side of the equation. -5ln + lnx + 2lnx = -2lnx + 2lnx Combine like terms: lnx + 2lnx = 3lnx -5ln + 3lnx = -2lnx + 2lnx Combine like terms: -2lnx + 2lnx = 0 -5ln + 3lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-5 + 3x) = 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 '(-5 + 3x)' equal to zero and attempt to solve: Simplifying -5 + 3x = 0 Solving -5 + 3x = 0 Move all terms containing l to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + 3x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 3x = 0 + 5 3x = 0 + 5 Combine like terms: 0 + 5 = 5 3x = 5 Add '-3x' to each side of the equation. 3x + -3x = 5 + -3x Combine like terms: 3x + -3x = 0 0 = 5 + -3x Simplifying 0 = 5 + -3x 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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