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