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