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Simplifying ln(x + -3) + -1ln(x + 3) = ln(x + -5) Reorder the terms: ln(-3 + x) + -1ln(x + 3) = ln(x + -5) (-3 * ln + x * ln) + -1ln(x + 3) = ln(x + -5) (-3ln + lnx) + -1ln(x + 3) = ln(x + -5) Reorder the terms: -3ln + lnx + -1ln(3 + x) = ln(x + -5) -3ln + lnx + (3 * -1ln + x * -1ln) = ln(x + -5) -3ln + lnx + (-3ln + -1lnx) = ln(x + -5) Reorder the terms: -3ln + -3ln + lnx + -1lnx = ln(x + -5) Combine like terms: -3ln + -3ln = -6ln -6ln + lnx + -1lnx = ln(x + -5) Combine like terms: lnx + -1lnx = 0 -6ln + 0 = ln(x + -5) -6ln = ln(x + -5) Reorder the terms: -6ln = ln(-5 + x) -6ln = (-5 * ln + x * ln) -6ln = (-5ln + lnx) Solving -6ln = -5ln + lnx 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. -6ln + 5ln = -5ln + 5ln + lnx Combine like terms: -6ln + 5ln = -1ln -1ln = -5ln + 5ln + lnx Combine like terms: -5ln + 5ln = 0 -1ln = 0 + lnx -1ln = lnx Add '-1lnx' to each side of the equation. -1ln + -1lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -1ln + -1lnx = 0 Factor out the Greatest Common Factor (GCF), '-1ln'. -1ln(1 + x) = 0 Ignore the factor -1.Subproblem 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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