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Simplifying ln(3 + -1x) * ln(x + 1) = 0 Reorder the terms: ln(3 + -1x) * ln(1 + x) = 0 Reorder the terms for easier multiplication: ln * ln(3 + -1x)(1 + x) = 0 Multiply ln * ln l2n2(3 + -1x)(1 + x) = 0 Multiply (3 + -1x) * (1 + x) l2n2(3(1 + x) + -1x * (1 + x)) = 0 l2n2((1 * 3 + x * 3) + -1x * (1 + x)) = 0 l2n2((3 + 3x) + -1x * (1 + x)) = 0 l2n2(3 + 3x + (1 * -1x + x * -1x)) = 0 l2n2(3 + 3x + (-1x + -1x2)) = 0 Combine like terms: 3x + -1x = 2x l2n2(3 + 2x + -1x2) = 0 (3 * l2n2 + 2x * l2n2 + -1x2 * l2n2) = 0 (3l2n2 + 2l2n2x + -1l2n2x2) = 0 Solving 3l2n2 + 2l2n2x + -1l2n2x2 = 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), 'l2n2'. l2n2(3 + 2x + -1x2) = 0 Factor a trinomial. l2n2((3 + -1x)(1 + x)) = 0Subproblem 1
Set the factor 'l2n2' equal to zero and attempt to solve: Simplifying l2n2 = 0 Solving l2n2 = 0 Move all terms containing l to the left, all other terms to the right. Simplifying l2n2 = 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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