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