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Simplifying 2ln(X + -2) = ln(5x) Reorder the terms: 2ln(-2 + X) = ln(5x) (-2 * 2ln + X * 2ln) = ln(5x) (-4ln + 2lnX) = ln(5x) Remove parenthesis around (5x) -4ln + 2lnX = ln * 5x Reorder the terms for easier multiplication: -4ln + 2lnX = 5ln * x Multiply ln * x -4ln + 2lnX = 5lnx Solving -4ln + 2lnX = 5lnx 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. -4ln + 2lnX + -5lnx = 5lnx + -5lnx Combine like terms: 5lnx + -5lnx = 0 -4ln + 2lnX + -5lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-4 + 2X + -5x) = 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 '(-4 + 2X + -5x)' equal to zero and attempt to solve: Simplifying -4 + 2X + -5x = 0 Solving -4 + 2X + -5x = 0 Move all terms containing l to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 2X + 4 + -5x = 0 + 4 Reorder the terms: -4 + 4 + 2X + -5x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 2X + -5x = 0 + 4 2X + -5x = 0 + 4 Combine like terms: 0 + 4 = 4 2X + -5x = 4 Add '-2X' to each side of the equation. 2X + -2X + -5x = 4 + -2X Combine like terms: 2X + -2X = 0 0 + -5x = 4 + -2X -5x = 4 + -2X Add '5x' to each side of the equation. -5x + 5x = 4 + -2X + 5x Combine like terms: -5x + 5x = 0 0 = 4 + -2X + 5x Simplifying 0 = 4 + -2X + 5x 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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