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