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