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Simplifying 5ln(x + -2) + -1ln(4 + -1x2) + -3ln(x) = 0 Reorder the terms: 5ln(-2 + x) + -1ln(4 + -1x2) + -3ln(x) = 0 (-2 * 5ln + x * 5ln) + -1ln(4 + -1x2) + -3ln(x) = 0 (-10ln + 5lnx) + -1ln(4 + -1x2) + -3ln(x) = 0 -10ln + 5lnx + (4 * -1ln + -1x2 * -1ln) + -3ln(x) = 0 -10ln + 5lnx + (-4ln + 1lnx2) + -3ln(x) = 0 Multiply ln * x -10ln + 5lnx + -4ln + 1lnx2 + -3lnx = 0 Reorder the terms: -10ln + -4ln + 5lnx + -3lnx + 1lnx2 = 0 Combine like terms: -10ln + -4ln = -14ln -14ln + 5lnx + -3lnx + 1lnx2 = 0 Combine like terms: 5lnx + -3lnx = 2lnx -14ln + 2lnx + 1lnx2 = 0 Solving -14ln + 2lnx + 1lnx2 = 0 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), 'ln'. ln(-14 + 2x + x2) = 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 '(-14 + 2x + x2)' equal to zero and attempt to solve: Simplifying -14 + 2x + x2 = 0 Solving -14 + 2x + x2 = 0 Move all terms containing l to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 2x + 14 + x2 = 0 + 14 Reorder the terms: -14 + 14 + 2x + x2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + 2x + x2 = 0 + 14 2x + x2 = 0 + 14 Combine like terms: 0 + 14 = 14 2x + x2 = 14 Add '-2x' to each side of the equation. 2x + -2x + x2 = 14 + -2x Combine like terms: 2x + -2x = 0 0 + x2 = 14 + -2x x2 = 14 + -2x Add '-1x2' to each side of the equation. x2 + -1x2 = 14 + -2x + -1x2 Combine like terms: x2 + -1x2 = 0 0 = 14 + -2x + -1x2 Simplifying 0 = 14 + -2x + -1x2 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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