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Simplifying 2ln(x) + -1ln(2x + -3) = ln(5x) + -1ln(x + 2) Multiply ln * x 2lnx + -1ln(2x + -3) = ln(5x) + -1ln(x + 2) Reorder the terms: 2lnx + -1ln(-3 + 2x) = ln(5x) + -1ln(x + 2) 2lnx + (-3 * -1ln + 2x * -1ln) = ln(5x) + -1ln(x + 2) 2lnx + (3ln + -2lnx) = ln(5x) + -1ln(x + 2) Reorder the terms: 3ln + 2lnx + -2lnx = ln(5x) + -1ln(x + 2) Combine like terms: 2lnx + -2lnx = 0 3ln + 0 = ln(5x) + -1ln(x + 2) 3ln = ln(5x) + -1ln(x + 2) Remove parenthesis around (5x) 3ln = ln * 5x + -1ln(x + 2) Reorder the terms for easier multiplication: 3ln = 5ln * x + -1ln(x + 2) Multiply ln * x 3ln = 5lnx + -1ln(x + 2) Reorder the terms: 3ln = 5lnx + -1ln(2 + x) 3ln = 5lnx + (2 * -1ln + x * -1ln) 3ln = 5lnx + (-2ln + -1lnx) Reorder the terms: 3ln = -2ln + 5lnx + -1lnx Combine like terms: 5lnx + -1lnx = 4lnx 3ln = -2ln + 4lnx Solving 3ln = -2ln + 4lnx 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. 3ln + 2ln = -2ln + 2ln + 4lnx Combine like terms: 3ln + 2ln = 5ln 5ln = -2ln + 2ln + 4lnx Combine like terms: -2ln + 2ln = 0 5ln = 0 + 4lnx 5ln = 4lnx Add '-4lnx' to each side of the equation. 5ln + -4lnx = 4lnx + -4lnx Combine like terms: 4lnx + -4lnx = 0 5ln + -4lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(5 + -4x) = 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 '(5 + -4x)' equal to zero and attempt to solve: Simplifying 5 + -4x = 0 Solving 5 + -4x = 0 Move all terms containing l to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -4x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4x = 0 + -5 -4x = 0 + -5 Combine like terms: 0 + -5 = -5 -4x = -5 Add '4x' to each side of the equation. -4x + 4x = -5 + 4x Combine like terms: -4x + 4x = 0 0 = -5 + 4x Simplifying 0 = -5 + 4x 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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