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Simplifying ln(x + 4) = ln(x + -9) + -1ln(x + 9) Reorder the terms: ln(4 + x) = ln(x + -9) + -1ln(x + 9) (4 * ln + x * ln) = ln(x + -9) + -1ln(x + 9) (4ln + lnx) = ln(x + -9) + -1ln(x + 9) Reorder the terms: 4ln + lnx = ln(-9 + x) + -1ln(x + 9) 4ln + lnx = (-9 * ln + x * ln) + -1ln(x + 9) 4ln + lnx = (-9ln + lnx) + -1ln(x + 9) Reorder the terms: 4ln + lnx = -9ln + lnx + -1ln(9 + x) 4ln + lnx = -9ln + lnx + (9 * -1ln + x * -1ln) 4ln + lnx = -9ln + lnx + (-9ln + -1lnx) Reorder the terms: 4ln + lnx = -9ln + -9ln + lnx + -1lnx Combine like terms: -9ln + -9ln = -18ln 4ln + lnx = -18ln + lnx + -1lnx Combine like terms: lnx + -1lnx = 0 4ln + lnx = -18ln + 0 4ln + lnx = -18ln Solving 4ln + lnx = -18ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '18ln' to each side of the equation. 4ln + 18ln + lnx = -18ln + 18ln Combine like terms: 4ln + 18ln = 22ln 22ln + lnx = -18ln + 18ln Combine like terms: -18ln + 18ln = 0 22ln + lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(22 + 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 '(22 + x)' equal to zero and attempt to solve: Simplifying 22 + x = 0 Solving 22 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-22' to each side of the equation. 22 + -22 + x = 0 + -22 Combine like terms: 22 + -22 = 0 0 + x = 0 + -22 x = 0 + -22 Combine like terms: 0 + -22 = -22 x = -22 Add '-1x' to each side of the equation. x + -1x = -22 + -1x Combine like terms: x + -1x = 0 0 = -22 + -1x Simplifying 0 = -22 + -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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