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Simplifying ln(x + -3) + lnx = ln(x + 5) Reorder the terms: ln(-3 + x) + lnx = ln(x + 5) (-3 * ln + x * ln) + lnx = ln(x + 5) (-3ln + lnx) + lnx = ln(x + 5) Combine like terms: lnx + lnx = 2lnx -3ln + 2lnx = ln(x + 5) Reorder the terms: -3ln + 2lnx = ln(5 + x) -3ln + 2lnx = (5 * ln + x * ln) -3ln + 2lnx = (5ln + lnx) Solving -3ln + 2lnx = 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 + 2lnx = 5ln + -5ln + lnx Combine like terms: -3ln + -5ln = -8ln -8ln + 2lnx = 5ln + -5ln + lnx Combine like terms: 5ln + -5ln = 0 -8ln + 2lnx = 0 + lnx -8ln + 2lnx = lnx Add '-1lnx' to each side of the equation. -8ln + 2lnx + -1lnx = lnx + -1lnx Combine like terms: 2lnx + -1lnx = 1lnx -8ln + 1lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -8ln + 1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-8 + x) = 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 + x)' equal to zero and attempt to solve: Simplifying -8 + x = 0 Solving -8 + x = 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 + x = 0 + 8 Combine like terms: -8 + 8 = 0 0 + x = 0 + 8 x = 0 + 8 Combine like terms: 0 + 8 = 8 x = 8 Add '-1x' to each side of the equation. x + -1x = 8 + -1x Combine like terms: x + -1x = 0 0 = 8 + -1x Simplifying 0 = 8 + -1x 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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