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Simplifying ln(x + -13) = 2ln(x + 3) Reorder the terms: ln(-13 + x) = 2ln(x + 3) (-13 * ln + x * ln) = 2ln(x + 3) (-13ln + lnx) = 2ln(x + 3) Reorder the terms: -13ln + lnx = 2ln(3 + x) -13ln + lnx = (3 * 2ln + x * 2ln) -13ln + lnx = (6ln + 2lnx) Solving -13ln + lnx = 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 + lnx = 6ln + -6ln + 2lnx Combine like terms: -13ln + -6ln = -19ln -19ln + lnx = 6ln + -6ln + 2lnx Combine like terms: 6ln + -6ln = 0 -19ln + lnx = 0 + 2lnx -19ln + lnx = 2lnx Add '-2lnx' to each side of the equation. -19ln + lnx + -2lnx = 2lnx + -2lnx Combine like terms: lnx + -2lnx = -1lnx -19ln + -1lnx = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 -19ln + -1lnx = 0 Factor out the Greatest Common Factor (GCF), '-1ln'. -1ln(19 + x) = 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 '(19 + x)' equal to zero and attempt to solve: Simplifying 19 + x = 0 Solving 19 + x = 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 + x = 0 + -19 Combine like terms: 19 + -19 = 0 0 + x = 0 + -19 x = 0 + -19 Combine like terms: 0 + -19 = -19 x = -19 Add '-1x' to each side of the equation. x + -1x = -19 + -1x Combine like terms: x + -1x = 0 0 = -19 + -1x Simplifying 0 = -19 + -1x 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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