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Simplifying ln(x3 + -2) = ln(4x2 + -5x) Reorder the terms: ln(-2 + x3) = ln(4x2 + -5x) (-2 * ln + x3 * ln) = ln(4x2 + -5x) (-2ln + lnx3) = ln(4x2 + -5x) Reorder the terms: -2ln + lnx3 = ln(-5x + 4x2) -2ln + lnx3 = (-5x * ln + 4x2 * ln) -2ln + lnx3 = (-5lnx + 4lnx2) Solving -2ln + lnx3 = -5lnx + 4lnx2 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '5lnx' to each side of the equation. -2ln + 5lnx + lnx3 = -5lnx + 5lnx + 4lnx2 Combine like terms: -5lnx + 5lnx = 0 -2ln + 5lnx + lnx3 = 0 + 4lnx2 -2ln + 5lnx + lnx3 = 4lnx2 Add '-4lnx2' to each side of the equation. -2ln + 5lnx + -4lnx2 + lnx3 = 4lnx2 + -4lnx2 Combine like terms: 4lnx2 + -4lnx2 = 0 -2ln + 5lnx + -4lnx2 + lnx3 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-2 + 5x + -4x2 + x3) = 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 + 5x + -4x2 + x3)' equal to zero and attempt to solve: Simplifying -2 + 5x + -4x2 + x3 = 0 Solving -2 + 5x + -4x2 + x3 = 0 Move all terms containing l to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 5x + -4x2 + 2 + x3 = 0 + 2 Reorder the terms: -2 + 2 + 5x + -4x2 + x3 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 5x + -4x2 + x3 = 0 + 2 5x + -4x2 + x3 = 0 + 2 Combine like terms: 0 + 2 = 2 5x + -4x2 + x3 = 2 Add '-5x' to each side of the equation. 5x + -4x2 + -5x + x3 = 2 + -5x Reorder the terms: 5x + -5x + -4x2 + x3 = 2 + -5x Combine like terms: 5x + -5x = 0 0 + -4x2 + x3 = 2 + -5x -4x2 + x3 = 2 + -5x Add '4x2' to each side of the equation. -4x2 + 4x2 + x3 = 2 + -5x + 4x2 Combine like terms: -4x2 + 4x2 = 0 0 + x3 = 2 + -5x + 4x2 x3 = 2 + -5x + 4x2 Add '-1x3' to each side of the equation. x3 + -1x3 = 2 + -5x + 4x2 + -1x3 Combine like terms: x3 + -1x3 = 0 0 = 2 + -5x + 4x2 + -1x3 Simplifying 0 = 2 + -5x + 4x2 + -1x3 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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