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Simplifying 4[lnz + ln(z + 5)] + -2ln(z + -5) = 0 Reorder the terms: 4[lnz + ln(5 + z)] + -2ln(z + -5) = 0 4[lnz + (5 * ln + z * ln)] + -2ln(z + -5) = 0 4[lnz + (5ln + lnz)] + -2ln(z + -5) = 0 Reorder the terms: 4[5ln + lnz + lnz] + -2ln(z + -5) = 0 Combine like terms: lnz + lnz = 2lnz 4[5ln + 2lnz] + -2ln(z + -5) = 0 [5ln * 4 + 2lnz * 4] + -2ln(z + -5) = 0 [20ln + 8lnz] + -2ln(z + -5) = 0 Reorder the terms: 20ln + 8lnz + -2ln(-5 + z) = 0 20ln + 8lnz + (-5 * -2ln + z * -2ln) = 0 20ln + 8lnz + (10ln + -2lnz) = 0 Reorder the terms: 20ln + 10ln + 8lnz + -2lnz = 0 Combine like terms: 20ln + 10ln = 30ln 30ln + 8lnz + -2lnz = 0 Combine like terms: 8lnz + -2lnz = 6lnz 30ln + 6lnz = 0 Solving 30ln + 6lnz = 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), '6ln'. 6ln(5 + z) = 0 Ignore the factor 6.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 '(5 + z)' equal to zero and attempt to solve: Simplifying 5 + z = 0 Solving 5 + z = 0 Move all terms containing l to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + z = 0 + -5 Combine like terms: 5 + -5 = 0 0 + z = 0 + -5 z = 0 + -5 Combine like terms: 0 + -5 = -5 z = -5 Add '-1z' to each side of the equation. z + -1z = -5 + -1z Combine like terms: z + -1z = 0 0 = -5 + -1z Simplifying 0 = -5 + -1z 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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