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