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Simplifying 2ln(x + -3) + -1ln(x + -5) = ln(18 + -1x) Reorder the terms: 2ln(-3 + x) + -1ln(x + -5) = ln(18 + -1x) (-3 * 2ln + x * 2ln) + -1ln(x + -5) = ln(18 + -1x) (-6ln + 2lnx) + -1ln(x + -5) = ln(18 + -1x) Reorder the terms: -6ln + 2lnx + -1ln(-5 + x) = ln(18 + -1x) -6ln + 2lnx + (-5 * -1ln + x * -1ln) = ln(18 + -1x) -6ln + 2lnx + (5ln + -1lnx) = ln(18 + -1x) Reorder the terms: -6ln + 5ln + 2lnx + -1lnx = ln(18 + -1x) Combine like terms: -6ln + 5ln = -1ln -1ln + 2lnx + -1lnx = ln(18 + -1x) Combine like terms: 2lnx + -1lnx = 1lnx -1ln + 1lnx = ln(18 + -1x) -1ln + 1lnx = (18 * ln + -1x * ln) -1ln + 1lnx = (18ln + -1lnx) Solving -1ln + 1lnx = 18ln + -1lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-18ln' to each side of the equation. -1ln + -18ln + 1lnx = 18ln + -18ln + -1lnx Combine like terms: -1ln + -18ln = -19ln -19ln + 1lnx = 18ln + -18ln + -1lnx Combine like terms: 18ln + -18ln = 0 -19ln + 1lnx = 0 + -1lnx -19ln + 1lnx = -1lnx Add 'lnx' to each side of the equation. -19ln + 1lnx + lnx = -1lnx + lnx Combine like terms: 1lnx + lnx = 2lnx -19ln + 2lnx = -1lnx + lnx Combine like terms: -1lnx + lnx = 0 -19ln + 2lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-19 + 2x) = 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 '(-19 + 2x)' equal to zero and attempt to solve: Simplifying -19 + 2x = 0 Solving -19 + 2x = 0 Move all terms containing l to the left, all other terms to the right. Add '19' to each side of the equation. -19 + 19 + 2x = 0 + 19 Combine like terms: -19 + 19 = 0 0 + 2x = 0 + 19 2x = 0 + 19 Combine like terms: 0 + 19 = 19 2x = 19 Add '-2x' to each side of the equation. 2x + -2x = 19 + -2x Combine like terms: 2x + -2x = 0 0 = 19 + -2x Simplifying 0 = 19 + -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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