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