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