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