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Simplifying 0 = ln(x2 + 4x + 3) + -1ln(x + 1) Reorder the terms: 0 = ln(3 + 4x + x2) + -1ln(x + 1) 0 = (3 * ln + 4x * ln + x2 * ln) + -1ln(x + 1) 0 = (3ln + 4lnx + lnx2) + -1ln(x + 1) Reorder the terms: 0 = 3ln + 4lnx + lnx2 + -1ln(1 + x) 0 = 3ln + 4lnx + lnx2 + (1 * -1ln + x * -1ln) 0 = 3ln + 4lnx + lnx2 + (-1ln + -1lnx) Reorder the terms: 0 = 3ln + -1ln + 4lnx + -1lnx + lnx2 Combine like terms: 3ln + -1ln = 2ln 0 = 2ln + 4lnx + -1lnx + lnx2 Combine like terms: 4lnx + -1lnx = 3lnx 0 = 2ln + 3lnx + lnx2 Solving 0 = 2ln + 3lnx + lnx2 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. 0 + -2ln = 2ln + 3lnx + -2ln + lnx2 Remove the zero: -2ln = 2ln + 3lnx + -2ln + lnx2 Reorder the terms: -2ln = 2ln + -2ln + 3lnx + lnx2 Combine like terms: 2ln + -2ln = 0 -2ln = 0 + 3lnx + lnx2 -2ln = 3lnx + lnx2 Add '-3lnx' to each side of the equation. -2ln + -3lnx = 3lnx + -3lnx + lnx2 Combine like terms: 3lnx + -3lnx = 0 -2ln + -3lnx = 0 + lnx2 -2ln + -3lnx = lnx2 Add '-1lnx2' to each side of the equation. -2ln + -3lnx + -1lnx2 = lnx2 + -1lnx2 Combine like terms: lnx2 + -1lnx2 = 0 -2ln + -3lnx + -1lnx2 = 0 Factor out the Greatest Common Factor (GCF), '-1ln'. -1ln(2 + 3x + x2) = 0 Factor a trinomial. -1ln((2 + x)(1 + x)) = 0 Ignore the factor -1.Subproblem 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 '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Add '-1x' to each side of the equation. x + -1x = -2 + -1x Combine like terms: x + -1x = 0 0 = -2 + -1x Simplifying 0 = -2 + -1x 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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