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Simplifying ln(x + -3) + -1ln(x + 3) = ln(2x + -11) + -1ln(x + 5) Reorder the terms: ln(-3 + x) + -1ln(x + 3) = ln(2x + -11) + -1ln(x + 5) (-3 * ln + x * ln) + -1ln(x + 3) = ln(2x + -11) + -1ln(x + 5) (-3ln + lnx) + -1ln(x + 3) = ln(2x + -11) + -1ln(x + 5) Reorder the terms: -3ln + lnx + -1ln(3 + x) = ln(2x + -11) + -1ln(x + 5) -3ln + lnx + (3 * -1ln + x * -1ln) = ln(2x + -11) + -1ln(x + 5) -3ln + lnx + (-3ln + -1lnx) = ln(2x + -11) + -1ln(x + 5) Reorder the terms: -3ln + -3ln + lnx + -1lnx = ln(2x + -11) + -1ln(x + 5) Combine like terms: -3ln + -3ln = -6ln -6ln + lnx + -1lnx = ln(2x + -11) + -1ln(x + 5) Combine like terms: lnx + -1lnx = 0 -6ln + 0 = ln(2x + -11) + -1ln(x + 5) -6ln = ln(2x + -11) + -1ln(x + 5) Reorder the terms: -6ln = ln(-11 + 2x) + -1ln(x + 5) -6ln = (-11 * ln + 2x * ln) + -1ln(x + 5) -6ln = (-11ln + 2lnx) + -1ln(x + 5) Reorder the terms: -6ln = -11ln + 2lnx + -1ln(5 + x) -6ln = -11ln + 2lnx + (5 * -1ln + x * -1ln) -6ln = -11ln + 2lnx + (-5ln + -1lnx) Reorder the terms: -6ln = -11ln + -5ln + 2lnx + -1lnx Combine like terms: -11ln + -5ln = -16ln -6ln = -16ln + 2lnx + -1lnx Combine like terms: 2lnx + -1lnx = 1lnx -6ln = -16ln + 1lnx Solving -6ln = -16ln + 1lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '16ln' to each side of the equation. -6ln + 16ln = -16ln + 16ln + 1lnx Combine like terms: -6ln + 16ln = 10ln 10ln = -16ln + 16ln + 1lnx Combine like terms: -16ln + 16ln = 0 10ln = 0 + 1lnx 10ln = 1lnx Add '-1lnx' to each side of the equation. 10ln + -1lnx = 1lnx + -1lnx Combine like terms: 1lnx + -1lnx = 0 10ln + -1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(10 + -1x) = 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 '(10 + -1x)' equal to zero and attempt to solve: Simplifying 10 + -1x = 0 Solving 10 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1x = 0 + -10 -1x = 0 + -10 Combine like terms: 0 + -10 = -10 -1x = -10 Add 'x' to each side of the equation. -1x + x = -10 + x Combine like terms: -1x + x = 0 0 = -10 + x Simplifying 0 = -10 + x 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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