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Simplifying ln(8x2 + 10x + -3) + -1ln(4x + -1) = 0 Reorder the terms: ln(-3 + 10x + 8x2) + -1ln(4x + -1) = 0 (-3 * ln + 10x * ln + 8x2 * ln) + -1ln(4x + -1) = 0 (-3ln + 10lnx + 8lnx2) + -1ln(4x + -1) = 0 Reorder the terms: -3ln + 10lnx + 8lnx2 + -1ln(-1 + 4x) = 0 -3ln + 10lnx + 8lnx2 + (-1 * -1ln + 4x * -1ln) = 0 -3ln + 10lnx + 8lnx2 + (1ln + -4lnx) = 0 Reorder the terms: -3ln + 1ln + 10lnx + -4lnx + 8lnx2 = 0 Combine like terms: -3ln + 1ln = -2ln -2ln + 10lnx + -4lnx + 8lnx2 = 0 Combine like terms: 10lnx + -4lnx = 6lnx -2ln + 6lnx + 8lnx2 = 0 Solving -2ln + 6lnx + 8lnx2 = 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), '2ln'. 2ln(-1 + 3x + 4x2) = 0 Factor a trinomial. 2ln((-1 + -1x)(1 + -4x)) = 0 Ignore the factor 2.Subproblem 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 '(1 + -4x)' equal to zero and attempt to solve: Simplifying 1 + -4x = 0 Solving 1 + -4x = 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 + -4x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4x = 0 + -1 -4x = 0 + -1 Combine like terms: 0 + -1 = -1 -4x = -1 Add '4x' to each side of the equation. -4x + 4x = -1 + 4x Combine like terms: -4x + 4x = 0 0 = -1 + 4x Simplifying 0 = -1 + 4x 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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