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Simplifying ln(11x + -5) + -1ln(x + -2) = ln(x + 5) Reorder the terms: ln(-5 + 11x) + -1ln(x + -2) = ln(x + 5) (-5 * ln + 11x * ln) + -1ln(x + -2) = ln(x + 5) (-5ln + 11lnx) + -1ln(x + -2) = ln(x + 5) Reorder the terms: -5ln + 11lnx + -1ln(-2 + x) = ln(x + 5) -5ln + 11lnx + (-2 * -1ln + x * -1ln) = ln(x + 5) -5ln + 11lnx + (2ln + -1lnx) = ln(x + 5) Reorder the terms: -5ln + 2ln + 11lnx + -1lnx = ln(x + 5) Combine like terms: -5ln + 2ln = -3ln -3ln + 11lnx + -1lnx = ln(x + 5) Combine like terms: 11lnx + -1lnx = 10lnx -3ln + 10lnx = ln(x + 5) Reorder the terms: -3ln + 10lnx = ln(5 + x) -3ln + 10lnx = (5 * ln + x * ln) -3ln + 10lnx = (5ln + lnx) Solving -3ln + 10lnx = 5ln + lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-5ln' to each side of the equation. -3ln + -5ln + 10lnx = 5ln + -5ln + lnx Combine like terms: -3ln + -5ln = -8ln -8ln + 10lnx = 5ln + -5ln + lnx Combine like terms: 5ln + -5ln = 0 -8ln + 10lnx = 0 + lnx -8ln + 10lnx = lnx Add '-1lnx' to each side of the equation. -8ln + 10lnx + -1lnx = lnx + -1lnx Combine like terms: 10lnx + -1lnx = 9lnx -8ln + 9lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -8ln + 9lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-8 + 9x) = 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 '(-8 + 9x)' equal to zero and attempt to solve: Simplifying -8 + 9x = 0 Solving -8 + 9x = 0 Move all terms containing l to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + 9x = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 9x = 0 + 8 9x = 0 + 8 Combine like terms: 0 + 8 = 8 9x = 8 Add '-9x' to each side of the equation. 9x + -9x = 8 + -9x Combine like terms: 9x + -9x = 0 0 = 8 + -9x Simplifying 0 = 8 + -9x 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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