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