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