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