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