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Simplifying ln(x + 6) + -1lnx = ln(x + 2) Reorder the terms: ln(6 + x) + -1lnx = ln(x + 2) (6 * ln + x * ln) + -1lnx = ln(x + 2) (6ln + lnx) + -1lnx = ln(x + 2) Combine like terms: lnx + -1lnx = 0 6ln + 0 = ln(x + 2) 6ln = ln(x + 2) Reorder the terms: 6ln = ln(2 + x) 6ln = (2 * ln + x * ln) 6ln = (2ln + lnx) Solving 6ln = 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. 6ln + -2ln = 2ln + -2ln + lnx Combine like terms: 6ln + -2ln = 4ln 4ln = 2ln + -2ln + lnx Combine like terms: 2ln + -2ln = 0 4ln = 0 + lnx 4ln = lnx Add '-1lnx' to each side of the equation. 4ln + -1lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 4ln + -1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(4 + -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 '(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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