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Simplifying 2lnx + -1ln(2x + -5) = ln(3x) + -1ln(x + -2) Reorder the terms: 2lnx + -1ln(-5 + 2x) = ln(3x) + -1ln(x + -2) 2lnx + (-5 * -1ln + 2x * -1ln) = ln(3x) + -1ln(x + -2) 2lnx + (5ln + -2lnx) = ln(3x) + -1ln(x + -2) Reorder the terms: 5ln + 2lnx + -2lnx = ln(3x) + -1ln(x + -2) Combine like terms: 2lnx + -2lnx = 0 5ln + 0 = ln(3x) + -1ln(x + -2) 5ln = ln(3x) + -1ln(x + -2) Remove parenthesis around (3x) 5ln = ln * 3x + -1ln(x + -2) Reorder the terms for easier multiplication: 5ln = 3ln * x + -1ln(x + -2) Multiply ln * x 5ln = 3lnx + -1ln(x + -2) Reorder the terms: 5ln = 3lnx + -1ln(-2 + x) 5ln = 3lnx + (-2 * -1ln + x * -1ln) 5ln = 3lnx + (2ln + -1lnx) Reorder the terms: 5ln = 2ln + 3lnx + -1lnx Combine like terms: 3lnx + -1lnx = 2lnx 5ln = 2ln + 2lnx Solving 5ln = 2ln + 2lnx 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. 5ln + -2ln = 2ln + -2ln + 2lnx Combine like terms: 5ln + -2ln = 3ln 3ln = 2ln + -2ln + 2lnx Combine like terms: 2ln + -2ln = 0 3ln = 0 + 2lnx 3ln = 2lnx Add '-2lnx' to each side of the equation. 3ln + -2lnx = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 3ln + -2lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(3 + -2x) = 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)' 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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