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Simplifying ln(x + -2) + -1ln(4 + -1x) = 0 Reorder the terms: ln(-2 + x) + -1ln(4 + -1x) = 0 (-2 * ln + x * ln) + -1ln(4 + -1x) = 0 (-2ln + lnx) + -1ln(4 + -1x) = 0 -2ln + lnx + (4 * -1ln + -1x * -1ln) = 0 -2ln + lnx + (-4ln + 1lnx) = 0 Reorder the terms: -2ln + -4ln + lnx + 1lnx = 0 Combine like terms: -2ln + -4ln = -6ln -6ln + lnx + 1lnx = 0 Combine like terms: lnx + 1lnx = 2lnx -6ln + 2lnx = 0 Solving -6ln + 2lnx = 0 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(-3 + x) = 0 Ignore the factor 2.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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