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