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Simplifying ln(x + 2) + -1ln(x + -3) + ln(3) = 2ln(1 + -1x2) + lnx Reorder the terms: ln(2 + x) + -1ln(x + -3) + ln(3) = 2ln(1 + -1x2) + lnx (2 * ln + x * ln) + -1ln(x + -3) + ln(3) = 2ln(1 + -1x2) + lnx (2ln + lnx) + -1ln(x + -3) + ln(3) = 2ln(1 + -1x2) + lnx Reorder the terms: 2ln + lnx + -1ln(-3 + x) + ln(3) = 2ln(1 + -1x2) + lnx 2ln + lnx + (-3 * -1ln + x * -1ln) + ln(3) = 2ln(1 + -1x2) + lnx 2ln + lnx + (3ln + -1lnx) + ln(3) = 2ln(1 + -1x2) + lnx Reorder the terms for easier multiplication: 2ln + lnx + 3ln + -1lnx + 3ln = 2ln(1 + -1x2) + lnx Reorder the terms: 2ln + 3ln + 3ln + lnx + -1lnx = 2ln(1 + -1x2) + lnx Combine like terms: 2ln + 3ln = 5ln 5ln + 3ln + lnx + -1lnx = 2ln(1 + -1x2) + lnx Combine like terms: 5ln + 3ln = 8ln 8ln + lnx + -1lnx = 2ln(1 + -1x2) + lnx Combine like terms: lnx + -1lnx = 0 8ln + 0 = 2ln(1 + -1x2) + lnx 8ln = 2ln(1 + -1x2) + lnx 8ln = (1 * 2ln + -1x2 * 2ln) + lnx 8ln = (2ln + -2lnx2) + lnx Reorder the terms: 8ln = 2ln + lnx + -2lnx2 Solving 8ln = 2ln + lnx + -2lnx2 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. 8ln + -2ln = 2ln + lnx + -2ln + -2lnx2 Combine like terms: 8ln + -2ln = 6ln 6ln = 2ln + lnx + -2ln + -2lnx2 Reorder the terms: 6ln = 2ln + -2ln + lnx + -2lnx2 Combine like terms: 2ln + -2ln = 0 6ln = 0 + lnx + -2lnx2 6ln = lnx + -2lnx2 Add '-1lnx' to each side of the equation. 6ln + -1lnx = lnx + -1lnx + -2lnx2 Combine like terms: lnx + -1lnx = 0 6ln + -1lnx = 0 + -2lnx2 6ln + -1lnx = -2lnx2 Add '2lnx2' to each side of the equation. 6ln + -1lnx + 2lnx2 = -2lnx2 + 2lnx2 Combine like terms: -2lnx2 + 2lnx2 = 0 6ln + -1lnx + 2lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(6 + -1x + 2x2) = 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 '(6 + -1x + 2x2)' equal to zero and attempt to solve: Simplifying 6 + -1x + 2x2 = 0 Solving 6 + -1x + 2x2 = 0 Move all terms containing l to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -1x + -6 + 2x2 = 0 + -6 Reorder the terms: 6 + -6 + -1x + 2x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x + 2x2 = 0 + -6 -1x + 2x2 = 0 + -6 Combine like terms: 0 + -6 = -6 -1x + 2x2 = -6 Add 'x' to each side of the equation. -1x + x + 2x2 = -6 + x Combine like terms: -1x + x = 0 0 + 2x2 = -6 + x 2x2 = -6 + x Add '-2x2' to each side of the equation. 2x2 + -2x2 = -6 + x + -2x2 Combine like terms: 2x2 + -2x2 = 0 0 = -6 + x + -2x2 Simplifying 0 = -6 + x + -2x2 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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