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