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Simplifying ln(2x + -6) + -1ln(-1x + 14) = 0 Reorder the terms: ln(-6 + 2x) + -1ln(-1x + 14) = 0 (-6 * ln + 2x * ln) + -1ln(-1x + 14) = 0 (-6ln + 2lnx) + -1ln(-1x + 14) = 0 Reorder the terms: -6ln + 2lnx + -1ln(14 + -1x) = 0 -6ln + 2lnx + (14 * -1ln + -1x * -1ln) = 0 -6ln + 2lnx + (-14ln + 1lnx) = 0 Reorder the terms: -6ln + -14ln + 2lnx + 1lnx = 0 Combine like terms: -6ln + -14ln = -20ln -20ln + 2lnx + 1lnx = 0 Combine like terms: 2lnx + 1lnx = 3lnx -20ln + 3lnx = 0 Solving -20ln + 3lnx = 0 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), 'ln'. ln(-20 + 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 '(-20 + 3x)' equal to zero and attempt to solve: Simplifying -20 + 3x = 0 Solving -20 + 3x = 0 Move all terms containing l to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + 3x = 0 + 20 Combine like terms: -20 + 20 = 0 0 + 3x = 0 + 20 3x = 0 + 20 Combine like terms: 0 + 20 = 20 3x = 20 Add '-3x' to each side of the equation. 3x + -3x = 20 + -3x Combine like terms: 3x + -3x = 0 0 = 20 + -3x Simplifying 0 = 20 + -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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