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Simplifying ln(x + -1) + ln(x + 2) = ln(8 + -2x) Reorder the terms: ln(-1 + x) + ln(x + 2) = ln(8 + -2x) (-1 * ln + x * ln) + ln(x + 2) = ln(8 + -2x) (-1ln + lnx) + ln(x + 2) = ln(8 + -2x) Reorder the terms: -1ln + lnx + ln(2 + x) = ln(8 + -2x) -1ln + lnx + (2 * ln + x * ln) = ln(8 + -2x) -1ln + lnx + (2ln + lnx) = ln(8 + -2x) Reorder the terms: -1ln + 2ln + lnx + lnx = ln(8 + -2x) Combine like terms: -1ln + 2ln = 1ln 1ln + lnx + lnx = ln(8 + -2x) Combine like terms: lnx + lnx = 2lnx 1ln + 2lnx = ln(8 + -2x) 1ln + 2lnx = (8 * ln + -2x * ln) 1ln + 2lnx = (8ln + -2lnx) Solving 1ln + 2lnx = 8ln + -2lnx 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. 1ln + -8ln + 2lnx = 8ln + -8ln + -2lnx Combine like terms: 1ln + -8ln = -7ln -7ln + 2lnx = 8ln + -8ln + -2lnx Combine like terms: 8ln + -8ln = 0 -7ln + 2lnx = 0 + -2lnx -7ln + 2lnx = -2lnx Add '2lnx' to each side of the equation. -7ln + 2lnx + 2lnx = -2lnx + 2lnx Combine like terms: 2lnx + 2lnx = 4lnx -7ln + 4lnx = -2lnx + 2lnx Combine like terms: -2lnx + 2lnx = 0 -7ln + 4lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-7 + 4x) = 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 '(-7 + 4x)' equal to zero and attempt to solve: Simplifying -7 + 4x = 0 Solving -7 + 4x = 0 Move all terms containing l to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + 4x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 4x = 0 + 7 4x = 0 + 7 Combine like terms: 0 + 7 = 7 4x = 7 Add '-4x' to each side of the equation. 4x + -4x = 7 + -4x Combine like terms: 4x + -4x = 0 0 = 7 + -4x Simplifying 0 = 7 + -4x 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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