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