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Simplifying ln(x + 9) = ln(x + -3) + -1ln(x + 3) Reorder the terms: ln(9 + x) = ln(x + -3) + -1ln(x + 3) (9 * ln + x * ln) = ln(x + -3) + -1ln(x + 3) (9ln + lnx) = ln(x + -3) + -1ln(x + 3) Reorder the terms: 9ln + lnx = ln(-3 + x) + -1ln(x + 3) 9ln + lnx = (-3 * ln + x * ln) + -1ln(x + 3) 9ln + lnx = (-3ln + lnx) + -1ln(x + 3) Reorder the terms: 9ln + lnx = -3ln + lnx + -1ln(3 + x) 9ln + lnx = -3ln + lnx + (3 * -1ln + x * -1ln) 9ln + lnx = -3ln + lnx + (-3ln + -1lnx) Reorder the terms: 9ln + lnx = -3ln + -3ln + lnx + -1lnx Combine like terms: -3ln + -3ln = -6ln 9ln + lnx = -6ln + lnx + -1lnx Combine like terms: lnx + -1lnx = 0 9ln + lnx = -6ln + 0 9ln + lnx = -6ln Solving 9ln + lnx = -6ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '6ln' to each side of the equation. 9ln + 6ln + lnx = -6ln + 6ln Combine like terms: 9ln + 6ln = 15ln 15ln + lnx = -6ln + 6ln Combine like terms: -6ln + 6ln = 0 15ln + lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(15 + 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 '(15 + x)' equal to zero and attempt to solve: Simplifying 15 + x = 0 Solving 15 + x = 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 + x = 0 + -15 Combine like terms: 15 + -15 = 0 0 + x = 0 + -15 x = 0 + -15 Combine like terms: 0 + -15 = -15 x = -15 Add '-1x' to each side of the equation. x + -1x = -15 + -1x Combine like terms: x + -1x = 0 0 = -15 + -1x Simplifying 0 = -15 + -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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