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Simplifying ln(2x + -1) + ln(x + 4) = ln(6x + 2) Reorder the terms: ln(-1 + 2x) + ln(x + 4) = ln(6x + 2) (-1 * ln + 2x * ln) + ln(x + 4) = ln(6x + 2) (-1ln + 2lnx) + ln(x + 4) = ln(6x + 2) Reorder the terms: -1ln + 2lnx + ln(4 + x) = ln(6x + 2) -1ln + 2lnx + (4 * ln + x * ln) = ln(6x + 2) -1ln + 2lnx + (4ln + lnx) = ln(6x + 2) Reorder the terms: -1ln + 4ln + 2lnx + lnx = ln(6x + 2) Combine like terms: -1ln + 4ln = 3ln 3ln + 2lnx + lnx = ln(6x + 2) Combine like terms: 2lnx + lnx = 3lnx 3ln + 3lnx = ln(6x + 2) Reorder the terms: 3ln + 3lnx = ln(2 + 6x) 3ln + 3lnx = (2 * ln + 6x * ln) 3ln + 3lnx = (2ln + 6lnx) Solving 3ln + 3lnx = 2ln + 6lnx 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 + 6lnx Combine like terms: 3ln + -2ln = 1ln 1ln + 3lnx = 2ln + -2ln + 6lnx Combine like terms: 2ln + -2ln = 0 1ln + 3lnx = 0 + 6lnx 1ln + 3lnx = 6lnx Add '-6lnx' to each side of the equation. 1ln + 3lnx + -6lnx = 6lnx + -6lnx Combine like terms: 3lnx + -6lnx = -3lnx 1ln + -3lnx = 6lnx + -6lnx Combine like terms: 6lnx + -6lnx = 0 1ln + -3lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(1 + -3x) = 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 '(1 + -3x)' equal to zero and attempt to solve: Simplifying 1 + -3x = 0 Solving 1 + -3x = 0 Move all terms containing l to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -3x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3x = 0 + -1 -3x = 0 + -1 Combine like terms: 0 + -1 = -1 -3x = -1 Add '3x' to each side of the equation. -3x + 3x = -1 + 3x Combine like terms: -3x + 3x = 0 0 = -1 + 3x Simplifying 0 = -1 + 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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