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