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Simplifying ln(x + -1) + ln(x + -2) + ln(x + 3) = ln(6) Reorder the terms: ln(-1 + x) + ln(x + -2) + ln(x + 3) = ln(6) (-1 * ln + x * ln) + ln(x + -2) + ln(x + 3) = ln(6) (-1ln + lnx) + ln(x + -2) + ln(x + 3) = ln(6) Reorder the terms: -1ln + lnx + ln(-2 + x) + ln(x + 3) = ln(6) -1ln + lnx + (-2 * ln + x * ln) + ln(x + 3) = ln(6) -1ln + lnx + (-2ln + lnx) + ln(x + 3) = ln(6) Reorder the terms: -1ln + lnx + -2ln + lnx + ln(3 + x) = ln(6) -1ln + lnx + -2ln + lnx + (3 * ln + x * ln) = ln(6) -1ln + lnx + -2ln + lnx + (3ln + lnx) = ln(6) Reorder the terms: -1ln + -2ln + 3ln + lnx + lnx + lnx = ln(6) Combine like terms: -1ln + -2ln = -3ln -3ln + 3ln + lnx + lnx + lnx = ln(6) Combine like terms: -3ln + 3ln = 0 0 + lnx + lnx + lnx = ln(6) lnx + lnx + lnx = ln(6) Combine like terms: lnx + lnx = 2lnx 2lnx + lnx = ln(6) Combine like terms: 2lnx + lnx = 3lnx 3lnx = ln(6) Reorder the terms for easier multiplication: 3lnx = 6ln Solving 3lnx = 6ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-6ln' to each side of the equation. -6ln + 3lnx = 6ln + -6ln Combine like terms: 6ln + -6ln = 0 -6ln + 3lnx = 0 Factor out the Greatest Common Factor (GCF), '3ln'. 3ln(-2 + x) = 0 Ignore the factor 3.Subproblem 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 '(-2 + x)' equal to zero and attempt to solve: Simplifying -2 + x = 0 Solving -2 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + x = 0 + 2 x = 0 + 2 Combine like terms: 0 + 2 = 2 x = 2 Add '-1x' to each side of the equation. x + -1x = 2 + -1x Combine like terms: x + -1x = 0 0 = 2 + -1x Simplifying 0 = 2 + -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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