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Simplifying ln((x + 1)(x + 2)) = ln(18) Reorder the terms: ln((1 + x)(x + 2)) = ln(18) Reorder the terms: ln((1 + x)(2 + x)) = ln(18) Multiply (1 + x) * (2 + x) ln((1(2 + x) + x(2 + x))) = ln(18) ln(((2 * 1 + x * 1) + x(2 + x))) = ln(18) ln(((2 + 1x) + x(2 + x))) = ln(18) ln((2 + 1x + (2 * x + x * x))) = ln(18) ln((2 + 1x + (2x + x2))) = ln(18) Combine like terms: 1x + 2x = 3x ln((2 + 3x + x2)) = ln(18) (2 * ln + 3x * ln + x2 * ln) = ln(18) (2ln + 3lnx + lnx2) = ln(18) Reorder the terms for easier multiplication: 2ln + 3lnx + lnx2 = 18ln Solving 2ln + 3lnx + lnx2 = 18ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-18ln' to each side of the equation. 2ln + 3lnx + -18ln + lnx2 = 18ln + -18ln Reorder the terms: 2ln + -18ln + 3lnx + lnx2 = 18ln + -18ln Combine like terms: 2ln + -18ln = -16ln -16ln + 3lnx + lnx2 = 18ln + -18ln Combine like terms: 18ln + -18ln = 0 -16ln + 3lnx + lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-16 + 3x + 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 '(-16 + 3x + x2)' equal to zero and attempt to solve: Simplifying -16 + 3x + x2 = 0 Solving -16 + 3x + x2 = 0 Move all terms containing l to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 3x + 16 + x2 = 0 + 16 Reorder the terms: -16 + 16 + 3x + x2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 3x + x2 = 0 + 16 3x + x2 = 0 + 16 Combine like terms: 0 + 16 = 16 3x + x2 = 16 Add '-3x' to each side of the equation. 3x + -3x + x2 = 16 + -3x Combine like terms: 3x + -3x = 0 0 + x2 = 16 + -3x x2 = 16 + -3x Add '-1x2' to each side of the equation. x2 + -1x2 = 16 + -3x + -1x2 Combine like terms: x2 + -1x2 = 0 0 = 16 + -3x + -1x2 Simplifying 0 = 16 + -3x + -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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