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