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