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Simplifying ln(5x + -4x2) = ln(5 + -4x) (5x * ln + -4x2 * ln) = ln(5 + -4x) (5lnx + -4lnx2) = ln(5 + -4x) 5lnx + -4lnx2 = (5 * ln + -4x * ln) 5lnx + -4lnx2 = (5ln + -4lnx) Solving 5lnx + -4lnx2 = 5ln + -4lnx 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. 5lnx + -5ln + -4lnx2 = 5ln + -5ln + -4lnx Reorder the terms: -5ln + 5lnx + -4lnx2 = 5ln + -5ln + -4lnx Combine like terms: 5ln + -5ln = 0 -5ln + 5lnx + -4lnx2 = 0 + -4lnx -5ln + 5lnx + -4lnx2 = -4lnx Add '4lnx' to each side of the equation. -5ln + 5lnx + 4lnx + -4lnx2 = -4lnx + 4lnx Combine like terms: 5lnx + 4lnx = 9lnx -5ln + 9lnx + -4lnx2 = -4lnx + 4lnx Combine like terms: -4lnx + 4lnx = 0 -5ln + 9lnx + -4lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-5 + 9x + -4x2) = 0 Factor a trinomial. ln((-5 + 4x)(1 + -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 '(-5 + 4x)' equal to zero and attempt to solve: Simplifying -5 + 4x = 0 Solving -5 + 4x = 0 Move all terms containing l to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + 4x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 4x = 0 + 5 4x = 0 + 5 Combine like terms: 0 + 5 = 5 4x = 5 Add '-4x' to each side of the equation. 4x + -4x = 5 + -4x Combine like terms: 4x + -4x = 0 0 = 5 + -4x Simplifying 0 = 5 + -4x 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 + -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. The solution to this equation could not be determined.
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