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Simplifying ln(x + -4) + ln(x + 1) = ln(x + -8) Reorder the terms: ln(-4 + x) + ln(x + 1) = ln(x + -8) (-4 * ln + x * ln) + ln(x + 1) = ln(x + -8) (-4ln + lnx) + ln(x + 1) = ln(x + -8) Reorder the terms: -4ln + lnx + ln(1 + x) = ln(x + -8) -4ln + lnx + (1 * ln + x * ln) = ln(x + -8) -4ln + lnx + (1ln + lnx) = ln(x + -8) Reorder the terms: -4ln + 1ln + lnx + lnx = ln(x + -8) Combine like terms: -4ln + 1ln = -3ln -3ln + lnx + lnx = ln(x + -8) Combine like terms: lnx + lnx = 2lnx -3ln + 2lnx = ln(x + -8) Reorder the terms: -3ln + 2lnx = ln(-8 + x) -3ln + 2lnx = (-8 * ln + x * ln) -3ln + 2lnx = (-8ln + lnx) Solving -3ln + 2lnx = -8ln + lnx 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. -3ln + 8ln + 2lnx = -8ln + 8ln + lnx Combine like terms: -3ln + 8ln = 5ln 5ln + 2lnx = -8ln + 8ln + lnx Combine like terms: -8ln + 8ln = 0 5ln + 2lnx = 0 + lnx 5ln + 2lnx = lnx Add '-1lnx' to each side of the equation. 5ln + 2lnx + -1lnx = lnx + -1lnx Combine like terms: 2lnx + -1lnx = 1lnx 5ln + 1lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 5ln + 1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(5 + 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 '(5 + x)' equal to zero and attempt to solve: Simplifying 5 + x = 0 Solving 5 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Add '-1x' to each side of the equation. x + -1x = -5 + -1x Combine like terms: x + -1x = 0 0 = -5 + -1x Simplifying 0 = -5 + -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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