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Simplifying ln(x + -1) + ln(x + 3) = ln(x + 27) Reorder the terms: ln(-1 + x) + ln(x + 3) = ln(x + 27) (-1 * ln + x * ln) + ln(x + 3) = ln(x + 27) (-1ln + lnx) + ln(x + 3) = ln(x + 27) Reorder the terms: -1ln + lnx + ln(3 + x) = ln(x + 27) -1ln + lnx + (3 * ln + x * ln) = ln(x + 27) -1ln + lnx + (3ln + lnx) = ln(x + 27) Reorder the terms: -1ln + 3ln + lnx + lnx = ln(x + 27) Combine like terms: -1ln + 3ln = 2ln 2ln + lnx + lnx = ln(x + 27) Combine like terms: lnx + lnx = 2lnx 2ln + 2lnx = ln(x + 27) Reorder the terms: 2ln + 2lnx = ln(27 + x) 2ln + 2lnx = (27 * ln + x * ln) 2ln + 2lnx = (27ln + lnx) Solving 2ln + 2lnx = 27ln + lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-27ln' to each side of the equation. 2ln + -27ln + 2lnx = 27ln + -27ln + lnx Combine like terms: 2ln + -27ln = -25ln -25ln + 2lnx = 27ln + -27ln + lnx Combine like terms: 27ln + -27ln = 0 -25ln + 2lnx = 0 + lnx -25ln + 2lnx = lnx Add '-1lnx' to each side of the equation. -25ln + 2lnx + -1lnx = lnx + -1lnx Combine like terms: 2lnx + -1lnx = 1lnx -25ln + 1lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -25ln + 1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-25 + 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 '(-25 + x)' equal to zero and attempt to solve: Simplifying -25 + x = 0 Solving -25 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + x = 0 + 25 Combine like terms: -25 + 25 = 0 0 + x = 0 + 25 x = 0 + 25 Combine like terms: 0 + 25 = 25 x = 25 Add '-1x' to each side of the equation. x + -1x = 25 + -1x Combine like terms: x + -1x = 0 0 = 25 + -1x Simplifying 0 = 25 + -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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