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Simplifying 2ln(x + -2) = ln(-3x + 24) Reorder the terms: 2ln(-2 + x) = ln(-3x + 24) (-2 * 2ln + x * 2ln) = ln(-3x + 24) (-4ln + 2lnx) = ln(-3x + 24) Reorder the terms: -4ln + 2lnx = ln(24 + -3x) -4ln + 2lnx = (24 * ln + -3x * ln) -4ln + 2lnx = (24ln + -3lnx) Solving -4ln + 2lnx = 24ln + -3lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-24ln' to each side of the equation. -4ln + -24ln + 2lnx = 24ln + -24ln + -3lnx Combine like terms: -4ln + -24ln = -28ln -28ln + 2lnx = 24ln + -24ln + -3lnx Combine like terms: 24ln + -24ln = 0 -28ln + 2lnx = 0 + -3lnx -28ln + 2lnx = -3lnx Add '3lnx' to each side of the equation. -28ln + 2lnx + 3lnx = -3lnx + 3lnx Combine like terms: 2lnx + 3lnx = 5lnx -28ln + 5lnx = -3lnx + 3lnx Combine like terms: -3lnx + 3lnx = 0 -28ln + 5lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-28 + 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 '(-28 + 5x)' equal to zero and attempt to solve: Simplifying -28 + 5x = 0 Solving -28 + 5x = 0 Move all terms containing l to the left, all other terms to the right. Add '28' to each side of the equation. -28 + 28 + 5x = 0 + 28 Combine like terms: -28 + 28 = 0 0 + 5x = 0 + 28 5x = 0 + 28 Combine like terms: 0 + 28 = 28 5x = 28 Add '-5x' to each side of the equation. 5x + -5x = 28 + -5x Combine like terms: 5x + -5x = 0 0 = 28 + -5x Simplifying 0 = 28 + -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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