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Simplifying ln(x + 3) + -1ln(3x + 9) = ln(2x + -1) Reorder the terms: ln(3 + x) + -1ln(3x + 9) = ln(2x + -1) (3 * ln + x * ln) + -1ln(3x + 9) = ln(2x + -1) (3ln + lnx) + -1ln(3x + 9) = ln(2x + -1) Reorder the terms: 3ln + lnx + -1ln(9 + 3x) = ln(2x + -1) 3ln + lnx + (9 * -1ln + 3x * -1ln) = ln(2x + -1) 3ln + lnx + (-9ln + -3lnx) = ln(2x + -1) Reorder the terms: 3ln + -9ln + lnx + -3lnx = ln(2x + -1) Combine like terms: 3ln + -9ln = -6ln -6ln + lnx + -3lnx = ln(2x + -1) Combine like terms: lnx + -3lnx = -2lnx -6ln + -2lnx = ln(2x + -1) Reorder the terms: -6ln + -2lnx = ln(-1 + 2x) -6ln + -2lnx = (-1 * ln + 2x * ln) -6ln + -2lnx = (-1ln + 2lnx) Solving -6ln + -2lnx = -1ln + 2lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add 'ln' to each side of the equation. -6ln + ln + -2lnx = -1ln + ln + 2lnx Combine like terms: -6ln + ln = -5ln -5ln + -2lnx = -1ln + ln + 2lnx Combine like terms: -1ln + ln = 0 -5ln + -2lnx = 0 + 2lnx -5ln + -2lnx = 2lnx Add '-2lnx' to each side of the equation. -5ln + -2lnx + -2lnx = 2lnx + -2lnx Combine like terms: -2lnx + -2lnx = -4lnx -5ln + -4lnx = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 -5ln + -4lnx = 0 Factor out the Greatest Common Factor (GCF), '-1ln'. -1ln(5 + 4x) = 0 Ignore the factor -1.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 '(5 + 4x)' equal to zero and attempt to solve: Simplifying 5 + 4x = 0 Solving 5 + 4x = 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 + 4x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 4x = 0 + -5 4x = 0 + -5 Combine like terms: 0 + -5 = -5 4x = -5 Add '-4x' to each side of the equation. 4x + -4x = -5 + -4x Combine like terms: 4x + -4x = 0 0 = -5 + -4x Simplifying 0 = -5 + -4x 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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