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Simplifying 2lnx + -1ln(2x + -9) = ln(5x) + -1ln(x + -4) Reorder the terms: 2lnx + -1ln(-9 + 2x) = ln(5x) + -1ln(x + -4) 2lnx + (-9 * -1ln + 2x * -1ln) = ln(5x) + -1ln(x + -4) 2lnx + (9ln + -2lnx) = ln(5x) + -1ln(x + -4) Reorder the terms: 9ln + 2lnx + -2lnx = ln(5x) + -1ln(x + -4) Combine like terms: 2lnx + -2lnx = 0 9ln + 0 = ln(5x) + -1ln(x + -4) 9ln = ln(5x) + -1ln(x + -4) Remove parenthesis around (5x) 9ln = ln * 5x + -1ln(x + -4) Reorder the terms for easier multiplication: 9ln = 5ln * x + -1ln(x + -4) Multiply ln * x 9ln = 5lnx + -1ln(x + -4) Reorder the terms: 9ln = 5lnx + -1ln(-4 + x) 9ln = 5lnx + (-4 * -1ln + x * -1ln) 9ln = 5lnx + (4ln + -1lnx) Reorder the terms: 9ln = 4ln + 5lnx + -1lnx Combine like terms: 5lnx + -1lnx = 4lnx 9ln = 4ln + 4lnx Solving 9ln = 4ln + 4lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-4ln' to each side of the equation. 9ln + -4ln = 4ln + -4ln + 4lnx Combine like terms: 9ln + -4ln = 5ln 5ln = 4ln + -4ln + 4lnx Combine like terms: 4ln + -4ln = 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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