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Simplifying 2ln(x + -4) = ln(5x) Reorder the terms: 2ln(-4 + x) = ln(5x) (-4 * 2ln + x * 2ln) = ln(5x) (-8ln + 2lnx) = ln(5x) Remove parenthesis around (5x) -8ln + 2lnx = ln * 5x Reorder the terms for easier multiplication: -8ln + 2lnx = 5ln * x Multiply ln * x -8ln + 2lnx = 5lnx Solving -8ln + 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. -8ln + 2lnx + -5lnx = 5lnx + -5lnx Combine like terms: 2lnx + -5lnx = -3lnx -8ln + -3lnx = 5lnx + -5lnx Combine like terms: 5lnx + -5lnx = 0 -8ln + -3lnx = 0 Factor out the Greatest Common Factor (GCF), '-1ln'. -1ln(8 + 3x) = 0 Ignore the factor -1.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 '(8 + 3x)' equal to zero and attempt to solve: Simplifying 8 + 3x = 0 Solving 8 + 3x = 0 Move all terms containing l to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + 3x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 3x = 0 + -8 3x = 0 + -8 Combine like terms: 0 + -8 = -8 3x = -8 Add '-3x' to each side of the equation. 3x + -3x = -8 + -3x Combine like terms: 3x + -3x = 0 0 = -8 + -3x Simplifying 0 = -8 + -3x 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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