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Simplifying Ln(x3 + x2 + -2) = ln(x3 + -1x + -1x2 + 1) Reorder the terms: nL(-2 + x2 + x3) = ln(x3 + -1x + -1x2 + 1) (-2 * nL + x2 * nL + x3 * nL) = ln(x3 + -1x + -1x2 + 1) (-2nL + nx2L + nx3L) = ln(x3 + -1x + -1x2 + 1) Reorder the terms: -2nL + nx2L + nx3L = ln(1 + -1x + -1x2 + x3) -2nL + nx2L + nx3L = (1 * ln + -1x * ln + -1x2 * ln + x3 * ln) -2nL + nx2L + nx3L = (1ln + -1lnx + -1lnx2 + lnx3) Solving -2nL + nx2L + nx3L = 1ln + -1lnx + -1lnx2 + lnx3 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-1ln' to each side of the equation. -2nL + nx2L + -1ln + nx3L = 1ln + -1lnx + -1lnx2 + -1ln + lnx3 Reorder the terms: -1ln + -2nL + nx2L + nx3L = 1ln + -1lnx + -1lnx2 + -1ln + lnx3 Reorder the terms: -1ln + -2nL + nx2L + nx3L = 1ln + -1ln + -1lnx + -1lnx2 + lnx3 Combine like terms: 1ln + -1ln = 0 -1ln + -2nL + nx2L + nx3L = 0 + -1lnx + -1lnx2 + lnx3 -1ln + -2nL + nx2L + nx3L = -1lnx + -1lnx2 + lnx3 Add 'lnx' to each side of the equation. -1ln + -2nL + nx2L + lnx + nx3L = -1lnx + -1lnx2 + lnx + lnx3 Reorder the terms: -1ln + lnx + -2nL + nx2L + nx3L = -1lnx + -1lnx2 + lnx + lnx3 Reorder the terms: -1ln + lnx + -2nL + nx2L + nx3L = -1lnx + lnx + -1lnx2 + lnx3 Combine like terms: -1lnx + lnx = 0 -1ln + lnx + -2nL + nx2L + nx3L = 0 + -1lnx2 + lnx3 -1ln + lnx + -2nL + nx2L + nx3L = -1lnx2 + lnx3 Add 'lnx2' to each side of the equation. -1ln + lnx + -2nL + nx2L + lnx2 + nx3L = -1lnx2 + lnx2 + lnx3 Reorder the terms: -1ln + lnx + lnx2 + -2nL + nx2L + nx3L = -1lnx2 + lnx2 + lnx3 Combine like terms: -1lnx2 + lnx2 = 0 -1ln + lnx + lnx2 + -2nL + nx2L + nx3L = 0 + lnx3 -1ln + lnx + lnx2 + -2nL + nx2L + nx3L = lnx3 Add '-1lnx3' to each side of the equation. -1ln + lnx + lnx2 + -2nL + nx2L + -1lnx3 + nx3L = lnx3 + -1lnx3 Reorder the terms: -1ln + lnx + lnx2 + -1lnx3 + -2nL + nx2L + nx3L = lnx3 + -1lnx3 Combine like terms: lnx3 + -1lnx3 = 0 -1ln + lnx + lnx2 + -1lnx3 + -2nL + nx2L + nx3L = 0 Factor out the Greatest Common Factor (GCF), 'n'. n(-1l + lx + lx2 + -1lx3 + -2L + x2L + x3L) = 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 '(-1l + lx + lx2 + -1lx3 + -2L + x2L + x3L)' equal to zero and attempt to solve: Simplifying -1l + lx + lx2 + -1lx3 + -2L + x2L + x3L = 0 Reorder the terms: -2L + -1l + lx + lx2 + -1lx3 + x2L + x3L = 0 Solving -2L + -1l + lx + lx2 + -1lx3 + x2L + x3L = 0 Move all terms containing n to the left, all other terms to the right. Add '2L' to each side of the equation. -2L + -1l + lx + lx2 + -1lx3 + x2L + 2L + x3L = 0 + 2L Reorder the terms: -2L + 2L + -1l + lx + lx2 + -1lx3 + x2L + x3L = 0 + 2L Combine like terms: -2L + 2L = 0 0 + -1l + lx + lx2 + -1lx3 + x2L + x3L = 0 + 2L -1l + lx + lx2 + -1lx3 + x2L + x3L = 0 + 2L Remove the zero: -1l + lx + lx2 + -1lx3 + x2L + x3L = 2L Add 'l' to each side of the equation. -1l + lx + lx2 + -1lx3 + x2L + l + x3L = 2L + l Reorder the terms: -1l + l + lx + lx2 + -1lx3 + x2L + x3L = 2L + l Combine like terms: -1l + l = 0 0 + lx + lx2 + -1lx3 + x2L + x3L = 2L + l lx + lx2 + -1lx3 + x2L + x3L = 2L + l Add '-1lx' to each side of the equation. lx + lx2 + -1lx3 + x2L + -1lx + x3L = 2L + l + -1lx Reorder the terms: lx + -1lx + lx2 + -1lx3 + x2L + x3L = 2L + l + -1lx Combine like terms: lx + -1lx = 0 0 + lx2 + -1lx3 + x2L + x3L = 2L + l + -1lx lx2 + -1lx3 + x2L + x3L = 2L + l + -1lx Add '-1lx2' to each side of the equation. lx2 + -1lx3 + x2L + -1lx2 + x3L = 2L + l + -1lx + -1lx2 Reorder the terms: lx2 + -1lx2 + -1lx3 + x2L + x3L = 2L + l + -1lx + -1lx2 Combine like terms: lx2 + -1lx2 = 0 0 + -1lx3 + x2L + x3L = 2L + l + -1lx + -1lx2 -1lx3 + x2L + x3L = 2L + l + -1lx + -1lx2 Add 'lx3' to each side of the equation. -1lx3 + x2L + lx3 + x3L = 2L + l + -1lx + -1lx2 + lx3 Reorder the terms: -1lx3 + lx3 + x2L + x3L = 2L + l + -1lx + -1lx2 + lx3 Combine like terms: -1lx3 + lx3 = 0 0 + x2L + x3L = 2L + l + -1lx + -1lx2 + lx3 x2L + x3L = 2L + l + -1lx + -1lx2 + lx3 Add '-1x2L' to each side of the equation. x2L + -1x2L + x3L = 2L + l + -1lx + -1lx2 + lx3 + -1x2L Combine like terms: x2L + -1x2L = 0 0 + x3L = 2L + l + -1lx + -1lx2 + lx3 + -1x2L x3L = 2L + l + -1lx + -1lx2 + lx3 + -1x2L Add '-1x3L' to each side of the equation. x3L + -1x3L = 2L + l + -1lx + -1lx2 + lx3 + -1x2L + -1x3L Combine like terms: x3L + -1x3L = 0 0 = 2L + l + -1lx + -1lx2 + lx3 + -1x2L + -1x3L Simplifying 0 = 2L + l + -1lx + -1lx2 + lx3 + -1x2L + -1x3L 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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