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