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Simplifying 2ln(x + 3) + 2ln(2x + 2) = 4ln(x + 2) Reorder the terms: 2ln(3 + x) + 2ln(2x + 2) = 4ln(x + 2) (3 * 2ln + x * 2ln) + 2ln(2x + 2) = 4ln(x + 2) (6ln + 2lnx) + 2ln(2x + 2) = 4ln(x + 2) Reorder the terms: 6ln + 2lnx + 2ln(2 + 2x) = 4ln(x + 2) 6ln + 2lnx + (2 * 2ln + 2x * 2ln) = 4ln(x + 2) 6ln + 2lnx + (4ln + 4lnx) = 4ln(x + 2) Reorder the terms: 6ln + 4ln + 2lnx + 4lnx = 4ln(x + 2) Combine like terms: 6ln + 4ln = 10ln 10ln + 2lnx + 4lnx = 4ln(x + 2) Combine like terms: 2lnx + 4lnx = 6lnx 10ln + 6lnx = 4ln(x + 2) Reorder the terms: 10ln + 6lnx = 4ln(2 + x) 10ln + 6lnx = (2 * 4ln + x * 4ln) 10ln + 6lnx = (8ln + 4lnx) Solving 10ln + 6lnx = 8ln + 4lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-8ln' to each side of the equation. 10ln + -8ln + 6lnx = 8ln + -8ln + 4lnx Combine like terms: 10ln + -8ln = 2ln 2ln + 6lnx = 8ln + -8ln + 4lnx Combine like terms: 8ln + -8ln = 0 2ln + 6lnx = 0 + 4lnx 2ln + 6lnx = 4lnx Add '-4lnx' to each side of the equation. 2ln + 6lnx + -4lnx = 4lnx + -4lnx Combine like terms: 6lnx + -4lnx = 2lnx 2ln + 2lnx = 4lnx + -4lnx Combine like terms: 4lnx + -4lnx = 0 2ln + 2lnx = 0 Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(1 + x) = 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 '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Add '-1x' to each side of the equation. x + -1x = -1 + -1x Combine like terms: x + -1x = 0 0 = -1 + -1x Simplifying 0 = -1 + -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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