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Simplifying ln(6x3 + -11x2 + -26x + 40) + -1ln(3x + -4) = ln(4x2 + -12x + 5) Reorder the terms: ln(40 + -26x + -11x2 + 6x3) + -1ln(3x + -4) = ln(4x2 + -12x + 5) (40 * ln + -26x * ln + -11x2 * ln + 6x3 * ln) + -1ln(3x + -4) = ln(4x2 + -12x + 5) (40ln + -26lnx + -11lnx2 + 6lnx3) + -1ln(3x + -4) = ln(4x2 + -12x + 5) Reorder the terms: 40ln + -26lnx + -11lnx2 + 6lnx3 + -1ln(-4 + 3x) = ln(4x2 + -12x + 5) 40ln + -26lnx + -11lnx2 + 6lnx3 + (-4 * -1ln + 3x * -1ln) = ln(4x2 + -12x + 5) 40ln + -26lnx + -11lnx2 + 6lnx3 + (4ln + -3lnx) = ln(4x2 + -12x + 5) Reorder the terms: 40ln + 4ln + -26lnx + -3lnx + -11lnx2 + 6lnx3 = ln(4x2 + -12x + 5) Combine like terms: 40ln + 4ln = 44ln 44ln + -26lnx + -3lnx + -11lnx2 + 6lnx3 = ln(4x2 + -12x + 5) Combine like terms: -26lnx + -3lnx = -29lnx 44ln + -29lnx + -11lnx2 + 6lnx3 = ln(4x2 + -12x + 5) Reorder the terms: 44ln + -29lnx + -11lnx2 + 6lnx3 = ln(5 + -12x + 4x2) 44ln + -29lnx + -11lnx2 + 6lnx3 = (5 * ln + -12x * ln + 4x2 * ln) 44ln + -29lnx + -11lnx2 + 6lnx3 = (5ln + -12lnx + 4lnx2) Solving 44ln + -29lnx + -11lnx2 + 6lnx3 = 5ln + -12lnx + 4lnx2 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. 44ln + -29lnx + -11lnx2 + -5ln + 6lnx3 = 5ln + -12lnx + -5ln + 4lnx2 Reorder the terms: 44ln + -5ln + -29lnx + -11lnx2 + 6lnx3 = 5ln + -12lnx + -5ln + 4lnx2 Combine like terms: 44ln + -5ln = 39ln 39ln + -29lnx + -11lnx2 + 6lnx3 = 5ln + -12lnx + -5ln + 4lnx2 Reorder the terms: 39ln + -29lnx + -11lnx2 + 6lnx3 = 5ln + -5ln + -12lnx + 4lnx2 Combine like terms: 5ln + -5ln = 0 39ln + -29lnx + -11lnx2 + 6lnx3 = 0 + -12lnx + 4lnx2 39ln + -29lnx + -11lnx2 + 6lnx3 = -12lnx + 4lnx2 Add '12lnx' to each side of the equation. 39ln + -29lnx + -11lnx2 + 12lnx + 6lnx3 = -12lnx + 12lnx + 4lnx2 Reorder the terms: 39ln + -29lnx + 12lnx + -11lnx2 + 6lnx3 = -12lnx + 12lnx + 4lnx2 Combine like terms: -29lnx + 12lnx = -17lnx 39ln + -17lnx + -11lnx2 + 6lnx3 = -12lnx + 12lnx + 4lnx2 Combine like terms: -12lnx + 12lnx = 0 39ln + -17lnx + -11lnx2 + 6lnx3 = 0 + 4lnx2 39ln + -17lnx + -11lnx2 + 6lnx3 = 4lnx2 Add '-4lnx2' to each side of the equation. 39ln + -17lnx + -11lnx2 + -4lnx2 + 6lnx3 = 4lnx2 + -4lnx2 Combine like terms: -11lnx2 + -4lnx2 = -15lnx2 39ln + -17lnx + -15lnx2 + 6lnx3 = 4lnx2 + -4lnx2 Combine like terms: 4lnx2 + -4lnx2 = 0 39ln + -17lnx + -15lnx2 + 6lnx3 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(39 + -17x + -15x2 + 6x3) = 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 '(39 + -17x + -15x2 + 6x3)' equal to zero and attempt to solve: Simplifying 39 + -17x + -15x2 + 6x3 = 0 Solving 39 + -17x + -15x2 + 6x3 = 0 Move all terms containing l to the left, all other terms to the right. Add '-39' to each side of the equation. 39 + -17x + -15x2 + -39 + 6x3 = 0 + -39 Reorder the terms: 39 + -39 + -17x + -15x2 + 6x3 = 0 + -39 Combine like terms: 39 + -39 = 0 0 + -17x + -15x2 + 6x3 = 0 + -39 -17x + -15x2 + 6x3 = 0 + -39 Combine like terms: 0 + -39 = -39 -17x + -15x2 + 6x3 = -39 Add '17x' to each side of the equation. -17x + -15x2 + 17x + 6x3 = -39 + 17x Reorder the terms: -17x + 17x + -15x2 + 6x3 = -39 + 17x Combine like terms: -17x + 17x = 0 0 + -15x2 + 6x3 = -39 + 17x -15x2 + 6x3 = -39 + 17x Add '15x2' to each side of the equation. -15x2 + 15x2 + 6x3 = -39 + 17x + 15x2 Combine like terms: -15x2 + 15x2 = 0 0 + 6x3 = -39 + 17x + 15x2 6x3 = -39 + 17x + 15x2 Add '-6x3' to each side of the equation. 6x3 + -6x3 = -39 + 17x + 15x2 + -6x3 Combine like terms: 6x3 + -6x3 = 0 0 = -39 + 17x + 15x2 + -6x3 Simplifying 0 = -39 + 17x + 15x2 + -6x3 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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