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Simplifying ln[(x + -2)(x + 2)] = ln(4 + 2x) Reorder the terms: ln[(-2 + x)(x + 2)] = ln(4 + 2x) Reorder the terms: ln[(-2 + x)(2 + x)] = ln(4 + 2x) Multiply (-2 + x) * (2 + x) ln[(-2(2 + x) + x(2 + x))] = ln(4 + 2x) ln[((2 * -2 + x * -2) + x(2 + x))] = ln(4 + 2x) ln[((-4 + -2x) + x(2 + x))] = ln(4 + 2x) ln[(-4 + -2x + (2 * x + x * x))] = ln(4 + 2x) ln[(-4 + -2x + (2x + x2))] = ln(4 + 2x) Combine like terms: -2x + 2x = 0 ln[(-4 + 0 + x2)] = ln(4 + 2x) ln[(-4 + x2)] = ln(4 + 2x) [-4 * ln + x2 * ln] = ln(4 + 2x) [-4ln + lnx2] = ln(4 + 2x) -4ln + lnx2 = (4 * ln + 2x * ln) -4ln + lnx2 = (4ln + 2lnx) Solving -4ln + lnx2 = 4ln + 2lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-4ln' to each side of the equation. -4ln + -4ln + lnx2 = 4ln + -4ln + 2lnx Combine like terms: -4ln + -4ln = -8ln -8ln + lnx2 = 4ln + -4ln + 2lnx Combine like terms: 4ln + -4ln = 0 -8ln + lnx2 = 0 + 2lnx -8ln + lnx2 = 2lnx Add '-2lnx' to each side of the equation. -8ln + -2lnx + lnx2 = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 -8ln + -2lnx + lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-8 + -2x + x2) = 0 Factor a trinomial. ln((-2 + -1x)(4 + -1x)) = 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 + -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.Subproblem 3
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Add 'x' to each side of the equation. -1x + x = -4 + x Combine like terms: -1x + x = 0 0 = -4 + x Simplifying 0 = -4 + 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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