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Simplifying 2ln(x + -1) = ln(-4x + 16) Reorder the terms: 2ln(-1 + x) = ln(-4x + 16) (-1 * 2ln + x * 2ln) = ln(-4x + 16) (-2ln + 2lnx) = ln(-4x + 16) Reorder the terms: -2ln + 2lnx = ln(16 + -4x) -2ln + 2lnx = (16 * ln + -4x * ln) -2ln + 2lnx = (16ln + -4lnx) Solving -2ln + 2lnx = 16ln + -4lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-16ln' to each side of the equation. -2ln + -16ln + 2lnx = 16ln + -16ln + -4lnx Combine like terms: -2ln + -16ln = -18ln -18ln + 2lnx = 16ln + -16ln + -4lnx Combine like terms: 16ln + -16ln = 0 -18ln + 2lnx = 0 + -4lnx -18ln + 2lnx = -4lnx Add '4lnx' to each side of the equation. -18ln + 2lnx + 4lnx = -4lnx + 4lnx Combine like terms: 2lnx + 4lnx = 6lnx -18ln + 6lnx = -4lnx + 4lnx Combine like terms: -4lnx + 4lnx = 0 -18ln + 6lnx = 0 Factor out the Greatest Common Factor (GCF), '6ln'. 6ln(-3 + x) = 0 Ignore the factor 6.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 '(-3 + x)' equal to zero and attempt to solve: Simplifying -3 + x = 0 Solving -3 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + x = 0 + 3 x = 0 + 3 Combine like terms: 0 + 3 = 3 x = 3 Add '-1x' to each side of the equation. x + -1x = 3 + -1x Combine like terms: x + -1x = 0 0 = 3 + -1x Simplifying 0 = 3 + -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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