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Simplifying ln(x + -3) = ln(18 + -2x) + -1ln(x + -4) Reorder the terms: ln(-3 + x) = ln(18 + -2x) + -1ln(x + -4) (-3 * ln + x * ln) = ln(18 + -2x) + -1ln(x + -4) (-3ln + lnx) = ln(18 + -2x) + -1ln(x + -4) -3ln + lnx = (18 * ln + -2x * ln) + -1ln(x + -4) -3ln + lnx = (18ln + -2lnx) + -1ln(x + -4) Reorder the terms: -3ln + lnx = 18ln + -2lnx + -1ln(-4 + x) -3ln + lnx = 18ln + -2lnx + (-4 * -1ln + x * -1ln) -3ln + lnx = 18ln + -2lnx + (4ln + -1lnx) Reorder the terms: -3ln + lnx = 18ln + 4ln + -2lnx + -1lnx Combine like terms: 18ln + 4ln = 22ln -3ln + lnx = 22ln + -2lnx + -1lnx Combine like terms: -2lnx + -1lnx = -3lnx -3ln + lnx = 22ln + -3lnx Solving -3ln + lnx = 22ln + -3lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-22ln' to each side of the equation. -3ln + -22ln + lnx = 22ln + -22ln + -3lnx Combine like terms: -3ln + -22ln = -25ln -25ln + lnx = 22ln + -22ln + -3lnx Combine like terms: 22ln + -22ln = 0 -25ln + lnx = 0 + -3lnx -25ln + lnx = -3lnx Add '3lnx' to each side of the equation. -25ln + lnx + 3lnx = -3lnx + 3lnx Combine like terms: lnx + 3lnx = 4lnx -25ln + 4lnx = -3lnx + 3lnx Combine like terms: -3lnx + 3lnx = 0 -25ln + 4lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-25 + 4x) = 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 '(-25 + 4x)' equal to zero and attempt to solve: Simplifying -25 + 4x = 0 Solving -25 + 4x = 0 Move all terms containing l to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + 4x = 0 + 25 Combine like terms: -25 + 25 = 0 0 + 4x = 0 + 25 4x = 0 + 25 Combine like terms: 0 + 25 = 25 4x = 25 Add '-4x' to each side of the equation. 4x + -4x = 25 + -4x Combine like terms: 4x + -4x = 0 0 = 25 + -4x Simplifying 0 = 25 + -4x 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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