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Simplifying 2ln(x + 3) = ln(13x + 3) Reorder the terms: 2ln(3 + x) = ln(13x + 3) (3 * 2ln + x * 2ln) = ln(13x + 3) (6ln + 2lnx) = ln(13x + 3) Reorder the terms: 6ln + 2lnx = ln(3 + 13x) 6ln + 2lnx = (3 * ln + 13x * ln) 6ln + 2lnx = (3ln + 13lnx) Solving 6ln + 2lnx = 3ln + 13lnx 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 + 13lnx Combine like terms: 6ln + -3ln = 3ln 3ln + 2lnx = 3ln + -3ln + 13lnx Combine like terms: 3ln + -3ln = 0 3ln + 2lnx = 0 + 13lnx 3ln + 2lnx = 13lnx Add '-13lnx' to each side of the equation. 3ln + 2lnx + -13lnx = 13lnx + -13lnx Combine like terms: 2lnx + -13lnx = -11lnx 3ln + -11lnx = 13lnx + -13lnx Combine like terms: 13lnx + -13lnx = 0 3ln + -11lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(3 + -11x) = 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 '(3 + -11x)' equal to zero and attempt to solve: Simplifying 3 + -11x = 0 Solving 3 + -11x = 0 Move all terms containing l to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -11x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -11x = 0 + -3 -11x = 0 + -3 Combine like terms: 0 + -3 = -3 -11x = -3 Add '11x' to each side of the equation. -11x + 11x = -3 + 11x Combine like terms: -11x + 11x = 0 0 = -3 + 11x Simplifying 0 = -3 + 11x 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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