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