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Simplifying ln(x + 2) = ln(x + 4) + -1ln(x + 5) Reorder the terms: ln(2 + x) = ln(x + 4) + -1ln(x + 5) (2 * ln + x * ln) = ln(x + 4) + -1ln(x + 5) (2ln + lnx) = ln(x + 4) + -1ln(x + 5) Reorder the terms: 2ln + lnx = ln(4 + x) + -1ln(x + 5) 2ln + lnx = (4 * ln + x * ln) + -1ln(x + 5) 2ln + lnx = (4ln + lnx) + -1ln(x + 5) Reorder the terms: 2ln + lnx = 4ln + lnx + -1ln(5 + x) 2ln + lnx = 4ln + lnx + (5 * -1ln + x * -1ln) 2ln + lnx = 4ln + lnx + (-5ln + -1lnx) Reorder the terms: 2ln + lnx = 4ln + -5ln + lnx + -1lnx Combine like terms: 4ln + -5ln = -1ln 2ln + lnx = -1ln + lnx + -1lnx Combine like terms: lnx + -1lnx = 0 2ln + lnx = -1ln + 0 2ln + lnx = -1ln Solving 2ln + lnx = -1ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add 'ln' to each side of the equation. 2ln + ln + lnx = -1ln + ln Combine like terms: 2ln + ln = 3ln 3ln + lnx = -1ln + ln Combine like terms: -1ln + ln = 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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