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Simplifying ln(x2 + -1) = ln(4x + -1) + -2ln(2) Reorder the terms: ln(-1 + x2) = ln(4x + -1) + -2ln(2) (-1 * ln + x2 * ln) = ln(4x + -1) + -2ln(2) (-1ln + lnx2) = ln(4x + -1) + -2ln(2) Reorder the terms: -1ln + lnx2 = ln(-1 + 4x) + -2ln(2) -1ln + lnx2 = (-1 * ln + 4x * ln) + -2ln(2) -1ln + lnx2 = (-1ln + 4lnx) + -2ln(2) Reorder the terms for easier multiplication: -1ln + lnx2 = -1ln + 4lnx + -2 * 2ln Multiply -2 * 2 -1ln + lnx2 = -1ln + 4lnx + -4ln Reorder the terms: -1ln + lnx2 = -1ln + -4ln + 4lnx Combine like terms: -1ln + -4ln = -5ln -1ln + lnx2 = -5ln + 4lnx Solving -1ln + lnx2 = -5ln + 4lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '5ln' to each side of the equation. -1ln + 5ln + lnx2 = -5ln + 5ln + 4lnx Combine like terms: -1ln + 5ln = 4ln 4ln + lnx2 = -5ln + 5ln + 4lnx Combine like terms: -5ln + 5ln = 0 4ln + lnx2 = 0 + 4lnx 4ln + lnx2 = 4lnx Add '-4lnx' to each side of the equation. 4ln + -4lnx + lnx2 = 4lnx + -4lnx Combine like terms: 4lnx + -4lnx = 0 4ln + -4lnx + lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(4 + -4x + x2) = 0 Factor a trinomial. ln((2 + -1x)(2 + -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 '(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. The solution to this equation could not be determined.
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