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Simplifying ln(13 + -3x) = 2ln(x + -3) (13 * ln + -3x * ln) = 2ln(x + -3) (13ln + -3lnx) = 2ln(x + -3) Reorder the terms: 13ln + -3lnx = 2ln(-3 + x) 13ln + -3lnx = (-3 * 2ln + x * 2ln) 13ln + -3lnx = (-6ln + 2lnx) Solving 13ln + -3lnx = -6ln + 2lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '6ln' to each side of the equation. 13ln + 6ln + -3lnx = -6ln + 6ln + 2lnx Combine like terms: 13ln + 6ln = 19ln 19ln + -3lnx = -6ln + 6ln + 2lnx Combine like terms: -6ln + 6ln = 0 19ln + -3lnx = 0 + 2lnx 19ln + -3lnx = 2lnx Add '-2lnx' to each side of the equation. 19ln + -3lnx + -2lnx = 2lnx + -2lnx Combine like terms: -3lnx + -2lnx = -5lnx 19ln + -5lnx = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 19ln + -5lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(19 + -5x) = 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 '(19 + -5x)' equal to zero and attempt to solve: Simplifying 19 + -5x = 0 Solving 19 + -5x = 0 Move all terms containing l to the left, all other terms to the right. Add '-19' to each side of the equation. 19 + -19 + -5x = 0 + -19 Combine like terms: 19 + -19 = 0 0 + -5x = 0 + -19 -5x = 0 + -19 Combine like terms: 0 + -19 = -19 -5x = -19 Add '5x' to each side of the equation. -5x + 5x = -19 + 5x Combine like terms: -5x + 5x = 0 0 = -19 + 5x Simplifying 0 = -19 + 5x 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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