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Simplifying ln(x + 6) = 2ln(x + -6) Reorder the terms: ln(6 + x) = 2ln(x + -6) (6 * ln + x * ln) = 2ln(x + -6) (6ln + lnx) = 2ln(x + -6) Reorder the terms: 6ln + lnx = 2ln(-6 + x) 6ln + lnx = (-6 * 2ln + x * 2ln) 6ln + lnx = (-12ln + 2lnx) Solving 6ln + lnx = -12ln + 2lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '12ln' to each side of the equation. 6ln + 12ln + lnx = -12ln + 12ln + 2lnx Combine like terms: 6ln + 12ln = 18ln 18ln + lnx = -12ln + 12ln + 2lnx Combine like terms: -12ln + 12ln = 0 18ln + lnx = 0 + 2lnx 18ln + lnx = 2lnx Add '-2lnx' to each side of the equation. 18ln + lnx + -2lnx = 2lnx + -2lnx Combine like terms: lnx + -2lnx = -1lnx 18ln + -1lnx = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 18ln + -1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(18 + -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 '(18 + -1x)' equal to zero and attempt to solve: Simplifying 18 + -1x = 0 Solving 18 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + -1x = 0 + -18 Combine like terms: 18 + -18 = 0 0 + -1x = 0 + -18 -1x = 0 + -18 Combine like terms: 0 + -18 = -18 -1x = -18 Add 'x' to each side of the equation. -1x + x = -18 + x Combine like terms: -1x + x = 0 0 = -18 + x Simplifying 0 = -18 + 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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