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Simplifying ln(4x2 + -1) = ln(x + 2) Reorder the terms: ln(-1 + 4x2) = ln(x + 2) (-1 * ln + 4x2 * ln) = ln(x + 2) (-1ln + 4lnx2) = ln(x + 2) Reorder the terms: -1ln + 4lnx2 = ln(2 + x) -1ln + 4lnx2 = (2 * ln + x * ln) -1ln + 4lnx2 = (2ln + lnx) Solving -1ln + 4lnx2 = 2ln + lnx 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. -1ln + -2ln + 4lnx2 = 2ln + -2ln + lnx Combine like terms: -1ln + -2ln = -3ln -3ln + 4lnx2 = 2ln + -2ln + lnx Combine like terms: 2ln + -2ln = 0 -3ln + 4lnx2 = 0 + lnx -3ln + 4lnx2 = lnx Add '-1lnx' to each side of the equation. -3ln + -1lnx + 4lnx2 = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -3ln + -1lnx + 4lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-3 + -1x + 4x2) = 0 Factor a trinomial. ln((-3 + -4x)(1 + -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 + -4x)' equal to zero and attempt to solve: Simplifying -3 + -4x = 0 Solving -3 + -4x = 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 + -4x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -4x = 0 + 3 -4x = 0 + 3 Combine like terms: 0 + 3 = 3 -4x = 3 Add '4x' to each side of the equation. -4x + 4x = 3 + 4x Combine like terms: -4x + 4x = 0 0 = 3 + 4x Simplifying 0 = 3 + 4x 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 '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 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 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Add 'x' to each side of the equation. -1x + x = -1 + x Combine like terms: -1x + x = 0 0 = -1 + x Simplifying 0 = -1 + 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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