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Simplifying ln(2n + 9) = ln(4n + -5) Reorder the terms: ln(9 + 2n) = ln(4n + -5) (9 * ln + 2n * ln) = ln(4n + -5) (9ln + 2ln2) = ln(4n + -5) Reorder the terms: 9ln + 2ln2 = ln(-5 + 4n) 9ln + 2ln2 = (-5 * ln + 4n * ln) 9ln + 2ln2 = (-5ln + 4ln2) Solving 9ln + 2ln2 = -5ln + 4ln2 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '5ln' to each side of the equation. 9ln + 5ln + 2ln2 = -5ln + 5ln + 4ln2 Combine like terms: 9ln + 5ln = 14ln 14ln + 2ln2 = -5ln + 5ln + 4ln2 Combine like terms: -5ln + 5ln = 0 14ln + 2ln2 = 0 + 4ln2 14ln + 2ln2 = 4ln2 Add '-4ln2' to each side of the equation. 14ln + 2ln2 + -4ln2 = 4ln2 + -4ln2 Combine like terms: 2ln2 + -4ln2 = -2ln2 14ln + -2ln2 = 4ln2 + -4ln2 Combine like terms: 4ln2 + -4ln2 = 0 14ln + -2ln2 = 0 Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(7 + -1n) = 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 '(7 + -1n)' equal to zero and attempt to solve: Simplifying 7 + -1n = 0 Solving 7 + -1n = 0 Move all terms containing l to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1n = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1n = 0 + -7 -1n = 0 + -7 Combine like terms: 0 + -7 = -7 -1n = -7 Add 'n' to each side of the equation. -1n + n = -7 + n Combine like terms: -1n + n = 0 0 = -7 + n Simplifying 0 = -7 + n 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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