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Simplifying lnx + -2ln(x + -3) = 2ln(x + -3) Reorder the terms: lnx + -2ln(-3 + x) = 2ln(x + -3) lnx + (-3 * -2ln + x * -2ln) = 2ln(x + -3) lnx + (6ln + -2lnx) = 2ln(x + -3) Reorder the terms: 6ln + lnx + -2lnx = 2ln(x + -3) Combine like terms: lnx + -2lnx = -1lnx 6ln + -1lnx = 2ln(x + -3) Reorder the terms: 6ln + -1lnx = 2ln(-3 + x) 6ln + -1lnx = (-3 * 2ln + x * 2ln) 6ln + -1lnx = (-6ln + 2lnx) Solving 6ln + -1lnx = -6ln + 2lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '6ln' to each side of the equation. 6ln + 6ln + -1lnx = -6ln + 6ln + 2lnx Combine like terms: 6ln + 6ln = 12ln 12ln + -1lnx = -6ln + 6ln + 2lnx Combine like terms: -6ln + 6ln = 0 12ln + -1lnx = 0 + 2lnx 12ln + -1lnx = 2lnx Add '-2lnx' to each side of the equation. 12ln + -1lnx + -2lnx = 2lnx + -2lnx Combine like terms: -1lnx + -2lnx = -3lnx 12ln + -3lnx = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 12ln + -3lnx = 0 Factor out the Greatest Common Factor (GCF), '3ln'. 3ln(4 + -1x) = 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 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 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 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Add 'x' to each side of the equation. -1x + x = -4 + x Combine like terms: -1x + x = 0 0 = -4 + x Simplifying 0 = -4 + 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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