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Simplifying ln[(x + 2)(x + -2)] = ln(2x + 11) Reorder the terms: ln[(2 + x)(x + -2)] = ln(2x + 11) Reorder the terms: ln[(2 + x)(-2 + x)] = ln(2x + 11) Multiply (2 + x) * (-2 + x) ln[(2(-2 + x) + x(-2 + x))] = ln(2x + 11) ln[((-2 * 2 + x * 2) + x(-2 + x))] = ln(2x + 11) ln[((-4 + 2x) + x(-2 + x))] = ln(2x + 11) ln[(-4 + 2x + (-2 * x + x * x))] = ln(2x + 11) ln[(-4 + 2x + (-2x + x2))] = ln(2x + 11) Combine like terms: 2x + -2x = 0 ln[(-4 + 0 + x2)] = ln(2x + 11) ln[(-4 + x2)] = ln(2x + 11) [-4 * ln + x2 * ln] = ln(2x + 11) [-4ln + lnx2] = ln(2x + 11) Reorder the terms: -4ln + lnx2 = ln(11 + 2x) -4ln + lnx2 = (11 * ln + 2x * ln) -4ln + lnx2 = (11ln + 2lnx) Solving -4ln + lnx2 = 11ln + 2lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-11ln' to each side of the equation. -4ln + -11ln + lnx2 = 11ln + -11ln + 2lnx Combine like terms: -4ln + -11ln = -15ln -15ln + lnx2 = 11ln + -11ln + 2lnx Combine like terms: 11ln + -11ln = 0 -15ln + lnx2 = 0 + 2lnx -15ln + lnx2 = 2lnx Add '-2lnx' to each side of the equation. -15ln + -2lnx + lnx2 = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 -15ln + -2lnx + lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-15 + -2x + x2) = 0 Factor a trinomial. ln((-3 + -1x)(5 + -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 '(-3 + -1x)' equal to zero and attempt to solve: Simplifying -3 + -1x = 0 Solving -3 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1x = 0 + 3 -1x = 0 + 3 Combine like terms: 0 + 3 = 3 -1x = 3 Add 'x' to each side of the equation. -1x + x = 3 + x Combine like terms: -1x + x = 0 0 = 3 + x Simplifying 0 = 3 + 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 '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Add 'x' to each side of the equation. -1x + x = -5 + x Combine like terms: -1x + x = 0 0 = -5 + x Simplifying 0 = -5 + 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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