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