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Simplifying ln(x + 5) = ln(x + -4) + -1ln(x + 4) Reorder the terms: ln(5 + x) = ln(x + -4) + -1ln(x + 4) (5 * ln + x * ln) = ln(x + -4) + -1ln(x + 4) (5ln + lnx) = ln(x + -4) + -1ln(x + 4) Reorder the terms: 5ln + lnx = ln(-4 + x) + -1ln(x + 4) 5ln + lnx = (-4 * ln + x * ln) + -1ln(x + 4) 5ln + lnx = (-4ln + lnx) + -1ln(x + 4) Reorder the terms: 5ln + lnx = -4ln + lnx + -1ln(4 + x) 5ln + lnx = -4ln + lnx + (4 * -1ln + x * -1ln) 5ln + lnx = -4ln + lnx + (-4ln + -1lnx) Reorder the terms: 5ln + lnx = -4ln + -4ln + lnx + -1lnx Combine like terms: -4ln + -4ln = -8ln 5ln + lnx = -8ln + lnx + -1lnx Combine like terms: lnx + -1lnx = 0 5ln + lnx = -8ln + 0 5ln + lnx = -8ln Solving 5ln + lnx = -8ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '8ln' to each side of the equation. 5ln + 8ln + lnx = -8ln + 8ln Combine like terms: 5ln + 8ln = 13ln 13ln + lnx = -8ln + 8ln Combine like terms: -8ln + 8ln = 0 13ln + lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(13 + 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 '(13 + x)' equal to zero and attempt to solve: Simplifying 13 + x = 0 Solving 13 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + x = 0 + -13 Combine like terms: 13 + -13 = 0 0 + x = 0 + -13 x = 0 + -13 Combine like terms: 0 + -13 = -13 x = -13 Add '-1x' to each side of the equation. x + -1x = -13 + -1x Combine like terms: x + -1x = 0 0 = -13 + -1x Simplifying 0 = -13 + -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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