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Simplifying Lny = Ln(1 + 3x) + -1ln(2 + x) nyL = (1 * nL + 3x * nL) + -1ln(2 + x) nyL = (1nL + 3nxL) + -1ln(2 + x) nyL = 1nL + 3nxL + (2 * -1ln + x * -1ln) nyL = 1nL + 3nxL + (-2ln + -1lnx) Reorder the terms: nyL = -2ln + -1lnx + 1nL + 3nxL Solving nyL = -2ln + -1lnx + 1nL + 3nxL Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '2ln' to each side of the equation. 2ln + nyL = -2ln + -1lnx + 1nL + 2ln + 3nxL Reorder the terms: 2ln + nyL = -2ln + 2ln + -1lnx + 1nL + 3nxL Combine like terms: -2ln + 2ln = 0 2ln + nyL = 0 + -1lnx + 1nL + 3nxL 2ln + nyL = -1lnx + 1nL + 3nxL Add 'lnx' to each side of the equation. 2ln + lnx + nyL = -1lnx + 1nL + lnx + 3nxL Reorder the terms: 2ln + lnx + nyL = -1lnx + lnx + 1nL + 3nxL Combine like terms: -1lnx + lnx = 0 2ln + lnx + nyL = 0 + 1nL + 3nxL 2ln + lnx + nyL = 1nL + 3nxL Add '-1nL' to each side of the equation. 2ln + lnx + -1nL + nyL = 1nL + -1nL + 3nxL Combine like terms: 1nL + -1nL = 0 2ln + lnx + -1nL + nyL = 0 + 3nxL 2ln + lnx + -1nL + nyL = 3nxL Add '-3nxL' to each side of the equation. 2ln + lnx + -1nL + -3nxL + nyL = 3nxL + -3nxL Combine like terms: 3nxL + -3nxL = 0 2ln + lnx + -1nL + -3nxL + nyL = 0 Factor out the Greatest Common Factor (GCF), 'n'. n(2l + lx + -1L + -3xL + yL) = 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 '(2l + lx + -1L + -3xL + yL)' equal to zero and attempt to solve: Simplifying 2l + lx + -1L + -3xL + yL = 0 Reorder the terms: -1L + 2l + lx + -3xL + yL = 0 Solving -1L + 2l + lx + -3xL + yL = 0 Move all terms containing n to the left, all other terms to the right. Add 'L' to each side of the equation. -1L + 2l + lx + -3xL + L + yL = 0 + L Reorder the terms: -1L + L + 2l + lx + -3xL + yL = 0 + L Combine like terms: -1L + L = 0 0 + 2l + lx + -3xL + yL = 0 + L 2l + lx + -3xL + yL = 0 + L Remove the zero: 2l + lx + -3xL + yL = L Add '-2l' to each side of the equation. 2l + lx + -3xL + -2l + yL = L + -2l Reorder the terms: 2l + -2l + lx + -3xL + yL = L + -2l Combine like terms: 2l + -2l = 0 0 + lx + -3xL + yL = L + -2l lx + -3xL + yL = L + -2l Add '-1lx' to each side of the equation. lx + -3xL + -1lx + yL = L + -2l + -1lx Reorder the terms: lx + -1lx + -3xL + yL = L + -2l + -1lx Combine like terms: lx + -1lx = 0 0 + -3xL + yL = L + -2l + -1lx -3xL + yL = L + -2l + -1lx Add '3xL' to each side of the equation. -3xL + 3xL + yL = L + -2l + -1lx + 3xL Combine like terms: -3xL + 3xL = 0 0 + yL = L + -2l + -1lx + 3xL yL = L + -2l + -1lx + 3xL Add '-1yL' to each side of the equation. yL + -1yL = L + -2l + -1lx + 3xL + -1yL Combine like terms: yL + -1yL = 0 0 = L + -2l + -1lx + 3xL + -1yL Simplifying 0 = L + -2l + -1lx + 3xL + -1yL 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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