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Simplifying Ln(5x + -2) = ln(2x + -5) Reorder the terms: nL(-2 + 5x) = ln(2x + -5) (-2 * nL + 5x * nL) = ln(2x + -5) (-2nL + 5nxL) = ln(2x + -5) Reorder the terms: -2nL + 5nxL = ln(-5 + 2x) -2nL + 5nxL = (-5 * ln + 2x * ln) -2nL + 5nxL = (-5ln + 2lnx) Solving -2nL + 5nxL = -5ln + 2lnx Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '5ln' to each side of the equation. -2nL + 5ln + 5nxL = -5ln + 5ln + 2lnx Reorder the terms: 5ln + -2nL + 5nxL = -5ln + 5ln + 2lnx Combine like terms: -5ln + 5ln = 0 5ln + -2nL + 5nxL = 0 + 2lnx 5ln + -2nL + 5nxL = 2lnx Add '-2lnx' to each side of the equation. 5ln + -2nL + -2lnx + 5nxL = 2lnx + -2lnx Reorder the terms: 5ln + -2lnx + -2nL + 5nxL = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 5ln + -2lnx + -2nL + 5nxL = 0 Factor out the Greatest Common Factor (GCF), 'n'. n(5l + -2lx + -2L + 5xL) = 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 '(5l + -2lx + -2L + 5xL)' equal to zero and attempt to solve: Simplifying 5l + -2lx + -2L + 5xL = 0 Reorder the terms: -2L + 5l + -2lx + 5xL = 0 Solving -2L + 5l + -2lx + 5xL = 0 Move all terms containing n to the left, all other terms to the right. Add '2L' to each side of the equation. -2L + 5l + -2lx + 2L + 5xL = 0 + 2L Reorder the terms: -2L + 2L + 5l + -2lx + 5xL = 0 + 2L Combine like terms: -2L + 2L = 0 0 + 5l + -2lx + 5xL = 0 + 2L 5l + -2lx + 5xL = 0 + 2L Remove the zero: 5l + -2lx + 5xL = 2L Add '-5l' to each side of the equation. 5l + -2lx + -5l + 5xL = 2L + -5l Reorder the terms: 5l + -5l + -2lx + 5xL = 2L + -5l Combine like terms: 5l + -5l = 0 0 + -2lx + 5xL = 2L + -5l -2lx + 5xL = 2L + -5l Add '2lx' to each side of the equation. -2lx + 2lx + 5xL = 2L + -5l + 2lx Combine like terms: -2lx + 2lx = 0 0 + 5xL = 2L + -5l + 2lx 5xL = 2L + -5l + 2lx Add '-5xL' to each side of the equation. 5xL + -5xL = 2L + -5l + 2lx + -5xL Combine like terms: 5xL + -5xL = 0 0 = 2L + -5l + 2lx + -5xL Simplifying 0 = 2L + -5l + 2lx + -5xL 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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