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Simplifying ln(x + 1) + ln(x + -1) + ln(x + 3) + -1ln(x2 + -1) = 0 Reorder the terms: ln(1 + x) + ln(x + -1) + ln(x + 3) + -1ln(x2 + -1) = 0 (1 * ln + x * ln) + ln(x + -1) + ln(x + 3) + -1ln(x2 + -1) = 0 (1ln + lnx) + ln(x + -1) + ln(x + 3) + -1ln(x2 + -1) = 0 Reorder the terms: 1ln + lnx + ln(-1 + x) + ln(x + 3) + -1ln(x2 + -1) = 0 1ln + lnx + (-1 * ln + x * ln) + ln(x + 3) + -1ln(x2 + -1) = 0 1ln + lnx + (-1ln + lnx) + ln(x + 3) + -1ln(x2 + -1) = 0 Reorder the terms: 1ln + lnx + -1ln + lnx + ln(3 + x) + -1ln(x2 + -1) = 0 1ln + lnx + -1ln + lnx + (3 * ln + x * ln) + -1ln(x2 + -1) = 0 1ln + lnx + -1ln + lnx + (3ln + lnx) + -1ln(x2 + -1) = 0 Reorder the terms: 1ln + lnx + -1ln + lnx + 3ln + lnx + -1ln(-1 + x2) = 0 1ln + lnx + -1ln + lnx + 3ln + lnx + (-1 * -1ln + x2 * -1ln) = 0 1ln + lnx + -1ln + lnx + 3ln + lnx + (1ln + -1lnx2) = 0 Reorder the terms: 1ln + -1ln + 3ln + 1ln + lnx + lnx + lnx + -1lnx2 = 0 Combine like terms: 1ln + -1ln = 0 0 + 3ln + 1ln + lnx + lnx + lnx + -1lnx2 = 0 3ln + 1ln + lnx + lnx + lnx + -1lnx2 = 0 Combine like terms: 3ln + 1ln = 4ln 4ln + lnx + lnx + lnx + -1lnx2 = 0 Combine like terms: lnx + lnx = 2lnx 4ln + 2lnx + lnx + -1lnx2 = 0 Combine like terms: 2lnx + lnx = 3lnx 4ln + 3lnx + -1lnx2 = 0 Solving 4ln + 3lnx + -1lnx2 = 0 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), 'ln'. ln(4 + 3x + -1x2) = 0 Factor a trinomial. ln((4 + -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 '(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.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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