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Simplifying ln(x + -1) + ln(x + 6) = ln(3x + 2) Reorder the terms: ln(-1 + x) + ln(x + 6) = ln(3x + 2) (-1 * ln + x * ln) + ln(x + 6) = ln(3x + 2) (-1ln + lnx) + ln(x + 6) = ln(3x + 2) Reorder the terms: -1ln + lnx + ln(6 + x) = ln(3x + 2) -1ln + lnx + (6 * ln + x * ln) = ln(3x + 2) -1ln + lnx + (6ln + lnx) = ln(3x + 2) Reorder the terms: -1ln + 6ln + lnx + lnx = ln(3x + 2) Combine like terms: -1ln + 6ln = 5ln 5ln + lnx + lnx = ln(3x + 2) Combine like terms: lnx + lnx = 2lnx 5ln + 2lnx = ln(3x + 2) Reorder the terms: 5ln + 2lnx = ln(2 + 3x) 5ln + 2lnx = (2 * ln + 3x * ln) 5ln + 2lnx = (2ln + 3lnx) Solving 5ln + 2lnx = 2ln + 3lnx 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 + 2lnx = 2ln + -2ln + 3lnx Combine like terms: 5ln + -2ln = 3ln 3ln + 2lnx = 2ln + -2ln + 3lnx Combine like terms: 2ln + -2ln = 0 3ln + 2lnx = 0 + 3lnx 3ln + 2lnx = 3lnx Add '-3lnx' to each side of the equation. 3ln + 2lnx + -3lnx = 3lnx + -3lnx Combine like terms: 2lnx + -3lnx = -1lnx 3ln + -1lnx = 3lnx + -3lnx Combine like terms: 3lnx + -3lnx = 0 3ln + -1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(3 + -1x) = 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 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 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 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Add 'x' to each side of the equation. -1x + x = -3 + x Combine like terms: -1x + x = 0 0 = -3 + x Simplifying 0 = -3 + x 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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