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Simplifying ln(7 + -1x) + -1ln(-4 + -1x) = ln(2 + -4x) (7 * ln + -1x * ln) + -1ln(-4 + -1x) = ln(2 + -4x) (7ln + -1lnx) + -1ln(-4 + -1x) = ln(2 + -4x) 7ln + -1lnx + (-4 * -1ln + -1x * -1ln) = ln(2 + -4x) 7ln + -1lnx + (4ln + 1lnx) = ln(2 + -4x) Reorder the terms: 7ln + 4ln + -1lnx + 1lnx = ln(2 + -4x) Combine like terms: 7ln + 4ln = 11ln 11ln + -1lnx + 1lnx = ln(2 + -4x) Combine like terms: -1lnx + 1lnx = 0 11ln + 0 = ln(2 + -4x) 11ln = ln(2 + -4x) 11ln = (2 * ln + -4x * ln) 11ln = (2ln + -4lnx) Solving 11ln = 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. 11ln + -2ln = 2ln + -2ln + -4lnx Combine like terms: 11ln + -2ln = 9ln 9ln = 2ln + -2ln + -4lnx Combine like terms: 2ln + -2ln = 0 9ln = 0 + -4lnx 9ln = -4lnx Add '4lnx' to each side of the equation. 9ln + 4lnx = -4lnx + 4lnx Combine like terms: -4lnx + 4lnx = 0 9ln + 4lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(9 + 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 '(9 + 4x)' equal to zero and attempt to solve: Simplifying 9 + 4x = 0 Solving 9 + 4x = 0 Move all terms containing l to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + 4x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 4x = 0 + -9 4x = 0 + -9 Combine like terms: 0 + -9 = -9 4x = -9 Add '-4x' to each side of the equation. 4x + -4x = -9 + -4x Combine like terms: 4x + -4x = 0 0 = -9 + -4x Simplifying 0 = -9 + -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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