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Simplifying ln(x + -5) + ln(x + 1) = ln(x + 9) Reorder the terms: ln(-5 + x) + ln(x + 1) = ln(x + 9) (-5 * ln + x * ln) + ln(x + 1) = ln(x + 9) (-5ln + lnx) + ln(x + 1) = ln(x + 9) Reorder the terms: -5ln + lnx + ln(1 + x) = ln(x + 9) -5ln + lnx + (1 * ln + x * ln) = ln(x + 9) -5ln + lnx + (1ln + lnx) = ln(x + 9) Reorder the terms: -5ln + 1ln + lnx + lnx = ln(x + 9) Combine like terms: -5ln + 1ln = -4ln -4ln + lnx + lnx = ln(x + 9) Combine like terms: lnx + lnx = 2lnx -4ln + 2lnx = ln(x + 9) Reorder the terms: -4ln + 2lnx = ln(9 + x) -4ln + 2lnx = (9 * ln + x * ln) -4ln + 2lnx = (9ln + lnx) Solving -4ln + 2lnx = 9ln + lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-9ln' to each side of the equation. -4ln + -9ln + 2lnx = 9ln + -9ln + lnx Combine like terms: -4ln + -9ln = -13ln -13ln + 2lnx = 9ln + -9ln + lnx Combine like terms: 9ln + -9ln = 0 -13ln + 2lnx = 0 + lnx -13ln + 2lnx = lnx Add '-1lnx' to each side of the equation. -13ln + 2lnx + -1lnx = lnx + -1lnx Combine like terms: 2lnx + -1lnx = 1lnx -13ln + 1lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -13ln + 1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-13 + 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 '(-13 + x)' equal to zero and attempt to solve: Simplifying -13 + x = 0 Solving -13 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + x = 0 + 13 Combine like terms: -13 + 13 = 0 0 + x = 0 + 13 x = 0 + 13 Combine like terms: 0 + 13 = 13 x = 13 Add '-1x' to each side of the equation. x + -1x = 13 + -1x Combine like terms: x + -1x = 0 0 = 13 + -1x Simplifying 0 = 13 + -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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