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Simplifying ln(x + -3) + ln(x + -5) = ln(8) Reorder the terms: ln(-3 + x) + ln(x + -5) = ln(8) (-3 * ln + x * ln) + ln(x + -5) = ln(8) (-3ln + lnx) + ln(x + -5) = ln(8) Reorder the terms: -3ln + lnx + ln(-5 + x) = ln(8) -3ln + lnx + (-5 * ln + x * ln) = ln(8) -3ln + lnx + (-5ln + lnx) = ln(8) Reorder the terms: -3ln + -5ln + lnx + lnx = ln(8) Combine like terms: -3ln + -5ln = -8ln -8ln + lnx + lnx = ln(8) Combine like terms: lnx + lnx = 2lnx -8ln + 2lnx = ln(8) Reorder the terms for easier multiplication: -8ln + 2lnx = 8ln Solving -8ln + 2lnx = 8ln 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. -8ln + -8ln + 2lnx = 8ln + -8ln Combine like terms: -8ln + -8ln = -16ln -16ln + 2lnx = 8ln + -8ln Combine like terms: 8ln + -8ln = 0 -16ln + 2lnx = 0 Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(-8 + x) = 0 Ignore the factor 2.Subproblem 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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