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Simplifying ln(x + -2) + ln(x + 2) + -1ln(x2) = -1ln(3) Reorder the terms: ln(-2 + x) + ln(x + 2) + -1ln(x2) = -1ln(3) (-2 * ln + x * ln) + ln(x + 2) + -1ln(x2) = -1ln(3) (-2ln + lnx) + ln(x + 2) + -1ln(x2) = -1ln(3) Reorder the terms: -2ln + lnx + ln(2 + x) + -1ln(x2) = -1ln(3) -2ln + lnx + (2 * ln + x * ln) + -1ln(x2) = -1ln(3) -2ln + lnx + (2ln + lnx) + -1ln(x2) = -1ln(3) Multiply ln * x2 -2ln + lnx + 2ln + lnx + -1lnx2 = -1ln(3) Reorder the terms: -2ln + 2ln + lnx + lnx + -1lnx2 = -1ln(3) Combine like terms: -2ln + 2ln = 0 0 + lnx + lnx + -1lnx2 = -1ln(3) lnx + lnx + -1lnx2 = -1ln(3) Combine like terms: lnx + lnx = 2lnx 2lnx + -1lnx2 = -1ln(3) Reorder the terms for easier multiplication: 2lnx + -1lnx2 = -1 * 3ln Multiply -1 * 3 2lnx + -1lnx2 = -3ln Solving 2lnx + -1lnx2 = -3ln 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. 2lnx + 3ln + -1lnx2 = -3ln + 3ln Reorder the terms: 3ln + 2lnx + -1lnx2 = -3ln + 3ln Combine like terms: -3ln + 3ln = 0 3ln + 2lnx + -1lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(3 + 2x + -1x2) = 0 Factor a trinomial. ln((3 + -1x)(1 + 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 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 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 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Add 'x' to each side of the equation. -1x + x = -3 + x Combine like terms: -1x + x = 0 0 = -3 + x Simplifying 0 = -3 + x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Add '-1x' to each side of the equation. x + -1x = -1 + -1x Combine like terms: x + -1x = 0 0 = -1 + -1x Simplifying 0 = -1 + -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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