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