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Simplifying ln(x + -2) + -1ln(x + 2) = ln(x + -1) + -1ln(2x + 4) Reorder the terms: ln(-2 + x) + -1ln(x + 2) = ln(x + -1) + -1ln(2x + 4) (-2 * ln + x * ln) + -1ln(x + 2) = ln(x + -1) + -1ln(2x + 4) (-2ln + lnx) + -1ln(x + 2) = ln(x + -1) + -1ln(2x + 4) Reorder the terms: -2ln + lnx + -1ln(2 + x) = ln(x + -1) + -1ln(2x + 4) -2ln + lnx + (2 * -1ln + x * -1ln) = ln(x + -1) + -1ln(2x + 4) -2ln + lnx + (-2ln + -1lnx) = ln(x + -1) + -1ln(2x + 4) Reorder the terms: -2ln + -2ln + lnx + -1lnx = ln(x + -1) + -1ln(2x + 4) Combine like terms: -2ln + -2ln = -4ln -4ln + lnx + -1lnx = ln(x + -1) + -1ln(2x + 4) Combine like terms: lnx + -1lnx = 0 -4ln + 0 = ln(x + -1) + -1ln(2x + 4) -4ln = ln(x + -1) + -1ln(2x + 4) Reorder the terms: -4ln = ln(-1 + x) + -1ln(2x + 4) -4ln = (-1 * ln + x * ln) + -1ln(2x + 4) -4ln = (-1ln + lnx) + -1ln(2x + 4) Reorder the terms: -4ln = -1ln + lnx + -1ln(4 + 2x) -4ln = -1ln + lnx + (4 * -1ln + 2x * -1ln) -4ln = -1ln + lnx + (-4ln + -2lnx) Reorder the terms: -4ln = -1ln + -4ln + lnx + -2lnx Combine like terms: -1ln + -4ln = -5ln -4ln = -5ln + lnx + -2lnx Combine like terms: lnx + -2lnx = -1lnx -4ln = -5ln + -1lnx Solving -4ln = -5ln + -1lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '5ln' to each side of the equation. -4ln + 5ln = -5ln + 5ln + -1lnx Combine like terms: -4ln + 5ln = 1ln 1ln = -5ln + 5ln + -1lnx Combine like terms: -5ln + 5ln = 0 1ln = 0 + -1lnx 1ln = -1lnx Add 'lnx' to each side of the equation. 1ln + lnx = -1lnx + lnx Combine like terms: -1lnx + lnx = 0 1ln + lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(1 + 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 '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Add '-1x' to each side of the equation. x + -1x = -1 + -1x Combine like terms: x + -1x = 0 0 = -1 + -1x Simplifying 0 = -1 + -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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