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Simplifying ln(4x + -4) = ln(8 + -5x) Reorder the terms: ln(-4 + 4x) = ln(8 + -5x) (-4 * ln + 4x * ln) = ln(8 + -5x) (-4ln + 4lnx) = ln(8 + -5x) -4ln + 4lnx = (8 * ln + -5x * ln) -4ln + 4lnx = (8ln + -5lnx) Solving -4ln + 4lnx = 8ln + -5lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-8ln' to each side of the equation. -4ln + -8ln + 4lnx = 8ln + -8ln + -5lnx Combine like terms: -4ln + -8ln = -12ln -12ln + 4lnx = 8ln + -8ln + -5lnx Combine like terms: 8ln + -8ln = 0 -12ln + 4lnx = 0 + -5lnx -12ln + 4lnx = -5lnx Add '5lnx' to each side of the equation. -12ln + 4lnx + 5lnx = -5lnx + 5lnx Combine like terms: 4lnx + 5lnx = 9lnx -12ln + 9lnx = -5lnx + 5lnx Combine like terms: -5lnx + 5lnx = 0 -12ln + 9lnx = 0 Factor out the Greatest Common Factor (GCF), '3ln'. 3ln(-4 + 3x) = 0 Ignore the factor 3.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 '(-4 + 3x)' equal to zero and attempt to solve: Simplifying -4 + 3x = 0 Solving -4 + 3x = 0 Move all terms containing l to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + 3x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 3x = 0 + 4 3x = 0 + 4 Combine like terms: 0 + 4 = 4 3x = 4 Add '-3x' to each side of the equation. 3x + -3x = 4 + -3x Combine like terms: 3x + -3x = 0 0 = 4 + -3x Simplifying 0 = 4 + -3x 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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