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