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Simplifying Ln(X + 9) = 2ln(X + -3) Reorder the terms: nL(9 + X) = 2ln(X + -3) (9 * nL + X * nL) = 2ln(X + -3) (9nL + nLX) = 2ln(X + -3) Reorder the terms: 9nL + nLX = 2ln(-3 + X) 9nL + nLX = (-3 * 2ln + X * 2ln) 9nL + nLX = (-6ln + 2lnX) Solving 9nL + nLX = -6ln + 2lnX Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '6ln' to each side of the equation. 9nL + 6ln + nLX = -6ln + 6ln + 2lnX Reorder the terms: 6ln + 9nL + nLX = -6ln + 6ln + 2lnX Combine like terms: -6ln + 6ln = 0 6ln + 9nL + nLX = 0 + 2lnX 6ln + 9nL + nLX = 2lnX Add '-2lnX' to each side of the equation. 6ln + 9nL + -2lnX + nLX = 2lnX + -2lnX Reorder the terms: 6ln + -2lnX + 9nL + nLX = 2lnX + -2lnX Combine like terms: 2lnX + -2lnX = 0 6ln + -2lnX + 9nL + nLX = 0 Factor out the Greatest Common Factor (GCF), 'n'. n(6l + -2lX + 9L + LX) = 0Subproblem 1
Set the factor 'n' equal to zero and attempt to solve: Simplifying n = 0 Solving n = 0 Move all terms containing n to the left, all other terms to the right. Simplifying n = 0Subproblem 2
Set the factor '(6l + -2lX + 9L + LX)' equal to zero and attempt to solve: Simplifying 6l + -2lX + 9L + LX = 0 Reorder the terms: 9L + LX + 6l + -2lX = 0 Solving 9L + LX + 6l + -2lX = 0 Move all terms containing n to the left, all other terms to the right. Add '-9L' to each side of the equation. 9L + LX + 6l + -9L + -2lX = 0 + -9L Reorder the terms: 9L + -9L + LX + 6l + -2lX = 0 + -9L Combine like terms: 9L + -9L = 0 0 + LX + 6l + -2lX = 0 + -9L LX + 6l + -2lX = 0 + -9L Remove the zero: LX + 6l + -2lX = -9L Add '-1LX' to each side of the equation. LX + 6l + -1LX + -2lX = -9L + -1LX Reorder the terms: LX + -1LX + 6l + -2lX = -9L + -1LX Combine like terms: LX + -1LX = 0 0 + 6l + -2lX = -9L + -1LX 6l + -2lX = -9L + -1LX Add '-6l' to each side of the equation. 6l + -6l + -2lX = -9L + -1LX + -6l Combine like terms: 6l + -6l = 0 0 + -2lX = -9L + -1LX + -6l -2lX = -9L + -1LX + -6l Add '2lX' to each side of the equation. -2lX + 2lX = -9L + -1LX + -6l + 2lX Combine like terms: -2lX + 2lX = 0 0 = -9L + -1LX + -6l + 2lX Simplifying 0 = -9L + -1LX + -6l + 2lX The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
n = {0}
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