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Simplifying ln(x + -1) = ln(5x + -7) + -1ln(x + -1) Reorder the terms: ln(-1 + x) = ln(5x + -7) + -1ln(x + -1) (-1 * ln + x * ln) = ln(5x + -7) + -1ln(x + -1) (-1ln + lnx) = ln(5x + -7) + -1ln(x + -1) Reorder the terms: -1ln + lnx = ln(-7 + 5x) + -1ln(x + -1) -1ln + lnx = (-7 * ln + 5x * ln) + -1ln(x + -1) -1ln + lnx = (-7ln + 5lnx) + -1ln(x + -1) Reorder the terms: -1ln + lnx = -7ln + 5lnx + -1ln(-1 + x) -1ln + lnx = -7ln + 5lnx + (-1 * -1ln + x * -1ln) -1ln + lnx = -7ln + 5lnx + (1ln + -1lnx) Reorder the terms: -1ln + lnx = -7ln + 1ln + 5lnx + -1lnx Combine like terms: -7ln + 1ln = -6ln -1ln + lnx = -6ln + 5lnx + -1lnx Combine like terms: 5lnx + -1lnx = 4lnx -1ln + lnx = -6ln + 4lnx Solving -1ln + lnx = -6ln + 4lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '6ln' to each side of the equation. -1ln + 6ln + lnx = -6ln + 6ln + 4lnx Combine like terms: -1ln + 6ln = 5ln 5ln + lnx = -6ln + 6ln + 4lnx Combine like terms: -6ln + 6ln = 0 5ln + lnx = 0 + 4lnx 5ln + lnx = 4lnx Add '-4lnx' to each side of the equation. 5ln + lnx + -4lnx = 4lnx + -4lnx Combine like terms: lnx + -4lnx = -3lnx 5ln + -3lnx = 4lnx + -4lnx Combine like terms: 4lnx + -4lnx = 0 5ln + -3lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(5 + -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 '(5 + -3x)' equal to zero and attempt to solve: Simplifying 5 + -3x = 0 Solving 5 + -3x = 0 Move all terms containing l to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -3x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3x = 0 + -5 -3x = 0 + -5 Combine like terms: 0 + -5 = -5 -3x = -5 Add '3x' to each side of the equation. -3x + 3x = -5 + 3x Combine like terms: -3x + 3x = 0 0 = -5 + 3x Simplifying 0 = -5 + 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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