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Simplifying ln(2x2 + 2) = 2ln(2x + -4) Reorder the terms: ln(2 + 2x2) = 2ln(2x + -4) (2 * ln + 2x2 * ln) = 2ln(2x + -4) (2ln + 2lnx2) = 2ln(2x + -4) Reorder the terms: 2ln + 2lnx2 = 2ln(-4 + 2x) 2ln + 2lnx2 = (-4 * 2ln + 2x * 2ln) 2ln + 2lnx2 = (-8ln + 4lnx) Solving 2ln + 2lnx2 = -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. 2ln + 8ln + 2lnx2 = -8ln + 8ln + 4lnx Combine like terms: 2ln + 8ln = 10ln 10ln + 2lnx2 = -8ln + 8ln + 4lnx Combine like terms: -8ln + 8ln = 0 10ln + 2lnx2 = 0 + 4lnx 10ln + 2lnx2 = 4lnx Add '-4lnx' to each side of the equation. 10ln + -4lnx + 2lnx2 = 4lnx + -4lnx Combine like terms: 4lnx + -4lnx = 0 10ln + -4lnx + 2lnx2 = 0 Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(5 + -2x + x2) = 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 '(5 + -2x + x2)' equal to zero and attempt to solve: Simplifying 5 + -2x + x2 = 0 Solving 5 + -2x + x2 = 0 Move all terms containing l to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -2x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + -2x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2x + x2 = 0 + -5 -2x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 -2x + x2 = -5 Add '2x' to each side of the equation. -2x + 2x + x2 = -5 + 2x Combine like terms: -2x + 2x = 0 0 + x2 = -5 + 2x x2 = -5 + 2x Add '-1x2' to each side of the equation. x2 + -1x2 = -5 + 2x + -1x2 Combine like terms: x2 + -1x2 = 0 0 = -5 + 2x + -1x2 Simplifying 0 = -5 + 2x + -1x2 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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