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Simplifying lnw + -3[4ln(w + -6) + -1ln(w + 6)] = 0 Reorder the terms: lnw + -3[4ln(-6 + w) + -1ln(w + 6)] = 0 lnw + -3[(-6 * 4ln + w * 4ln) + -1ln(w + 6)] = 0 lnw + -3[(-24ln + 4lnw) + -1ln(w + 6)] = 0 Reorder the terms: lnw + -3[-24ln + 4lnw + -1ln(6 + w)] = 0 lnw + -3[-24ln + 4lnw + (6 * -1ln + w * -1ln)] = 0 lnw + -3[-24ln + 4lnw + (-6ln + -1lnw)] = 0 Reorder the terms: lnw + -3[-24ln + -6ln + 4lnw + -1lnw] = 0 Combine like terms: -24ln + -6ln = -30ln lnw + -3[-30ln + 4lnw + -1lnw] = 0 Combine like terms: 4lnw + -1lnw = 3lnw lnw + -3[-30ln + 3lnw] = 0 lnw + [-30ln * -3 + 3lnw * -3] = 0 lnw + [90ln + -9lnw] = 0 Reorder the terms: 90ln + lnw + -9lnw = 0 Combine like terms: lnw + -9lnw = -8lnw 90ln + -8lnw = 0 Solving 90ln + -8lnw = 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(45 + -4w) = 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 '(45 + -4w)' equal to zero and attempt to solve: Simplifying 45 + -4w = 0 Solving 45 + -4w = 0 Move all terms containing l to the left, all other terms to the right. Add '-45' to each side of the equation. 45 + -45 + -4w = 0 + -45 Combine like terms: 45 + -45 = 0 0 + -4w = 0 + -45 -4w = 0 + -45 Combine like terms: 0 + -45 = -45 -4w = -45 Add '4w' to each side of the equation. -4w + 4w = -45 + 4w Combine like terms: -4w + 4w = 0 0 = -45 + 4w Simplifying 0 = -45 + 4w 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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