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Simplifying ln(-5x + -6) = ln(2 + -4x) Reorder the terms: ln(-6 + -5x) = ln(2 + -4x) (-6 * ln + -5x * ln) = ln(2 + -4x) (-6ln + -5lnx) = ln(2 + -4x) -6ln + -5lnx = (2 * ln + -4x * ln) -6ln + -5lnx = (2ln + -4lnx) Solving -6ln + -5lnx = 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. -6ln + -2ln + -5lnx = 2ln + -2ln + -4lnx Combine like terms: -6ln + -2ln = -8ln -8ln + -5lnx = 2ln + -2ln + -4lnx Combine like terms: 2ln + -2ln = 0 -8ln + -5lnx = 0 + -4lnx -8ln + -5lnx = -4lnx Add '4lnx' to each side of the equation. -8ln + -5lnx + 4lnx = -4lnx + 4lnx Combine like terms: -5lnx + 4lnx = -1lnx -8ln + -1lnx = -4lnx + 4lnx Combine like terms: -4lnx + 4lnx = 0 -8ln + -1lnx = 0 Factor out the Greatest Common Factor (GCF), '-1ln'. -1ln(8 + x) = 0 Ignore the factor -1.Subproblem 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 '(8 + x)' equal to zero and attempt to solve: Simplifying 8 + x = 0 Solving 8 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + x = 0 + -8 x = 0 + -8 Combine like terms: 0 + -8 = -8 x = -8 Add '-1x' to each side of the equation. x + -1x = -8 + -1x Combine like terms: x + -1x = 0 0 = -8 + -1x Simplifying 0 = -8 + -1x 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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