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