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Simplifying ln(x2 + -4) = ln(3x) Reorder the terms: ln(-4 + x2) = ln(3x) (-4 * ln + x2 * ln) = ln(3x) (-4ln + lnx2) = ln(3x) Remove parenthesis around (3x) -4ln + lnx2 = ln * 3x Reorder the terms for easier multiplication: -4ln + lnx2 = 3ln * x Multiply ln * x -4ln + lnx2 = 3lnx Solving -4ln + lnx2 = 3lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-3lnx' to each side of the equation. -4ln + -3lnx + lnx2 = 3lnx + -3lnx Combine like terms: 3lnx + -3lnx = 0 -4ln + -3lnx + lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-4 + -3x + x2) = 0 Factor a trinomial. ln((-1 + -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 '(-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.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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