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