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