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Simplifying lnw + -3[2ln(w + -6) + -1ln(w + 6)] = 0 Reorder the terms: lnw + -3[2ln(-6 + w) + -1ln(w + 6)] = 0 lnw + -3[(-6 * 2ln + w * 2ln) + -1ln(w + 6)] = 0 lnw + -3[(-12ln + 2lnw) + -1ln(w + 6)] = 0 Reorder the terms: lnw + -3[-12ln + 2lnw + -1ln(6 + w)] = 0 lnw + -3[-12ln + 2lnw + (6 * -1ln + w * -1ln)] = 0 lnw + -3[-12ln + 2lnw + (-6ln + -1lnw)] = 0 Reorder the terms: lnw + -3[-12ln + -6ln + 2lnw + -1lnw] = 0 Combine like terms: -12ln + -6ln = -18ln lnw + -3[-18ln + 2lnw + -1lnw] = 0 Combine like terms: 2lnw + -1lnw = 1lnw lnw + -3[-18ln + 1lnw] = 0 lnw + [-18ln * -3 + 1lnw * -3] = 0 lnw + [54ln + -3lnw] = 0 Reorder the terms: 54ln + lnw + -3lnw = 0 Combine like terms: lnw + -3lnw = -2lnw 54ln + -2lnw = 0 Solving 54ln + -2lnw = 0 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(27 + -1w) = 0 Ignore the factor 2.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 '(27 + -1w)' equal to zero and attempt to solve: Simplifying 27 + -1w = 0 Solving 27 + -1w = 0 Move all terms containing l to the left, all other terms to the right. Add '-27' to each side of the equation. 27 + -27 + -1w = 0 + -27 Combine like terms: 27 + -27 = 0 0 + -1w = 0 + -27 -1w = 0 + -27 Combine like terms: 0 + -27 = -27 -1w = -27 Add 'w' to each side of the equation. -1w + w = -27 + w Combine like terms: -1w + w = 0 0 = -27 + w Simplifying 0 = -27 + w 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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