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