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Simplifying Ln(5x + -1) = ln(10x + 4) Reorder the terms: nL(-1 + 5x) = ln(10x + 4) (-1 * nL + 5x * nL) = ln(10x + 4) (-1nL + 5nxL) = ln(10x + 4) Reorder the terms: -1nL + 5nxL = ln(4 + 10x) -1nL + 5nxL = (4 * ln + 10x * ln) -1nL + 5nxL = (4ln + 10lnx) Solving -1nL + 5nxL = 4ln + 10lnx Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-4ln' to each side of the equation. -1nL + -4ln + 5nxL = 4ln + -4ln + 10lnx Reorder the terms: -4ln + -1nL + 5nxL = 4ln + -4ln + 10lnx Combine like terms: 4ln + -4ln = 0 -4ln + -1nL + 5nxL = 0 + 10lnx -4ln + -1nL + 5nxL = 10lnx Add '-10lnx' to each side of the equation. -4ln + -1nL + -10lnx + 5nxL = 10lnx + -10lnx Reorder the terms: -4ln + -10lnx + -1nL + 5nxL = 10lnx + -10lnx Combine like terms: 10lnx + -10lnx = 0 -4ln + -10lnx + -1nL + 5nxL = 0 Factor out the Greatest Common Factor (GCF), 'n'. n(-4l + -10lx + -1L + 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 '(-4l + -10lx + -1L + 5xL)' equal to zero and attempt to solve: Simplifying -4l + -10lx + -1L + 5xL = 0 Reorder the terms: -1L + -4l + -10lx + 5xL = 0 Solving -1L + -4l + -10lx + 5xL = 0 Move all terms containing n to the left, all other terms to the right. Add 'L' to each side of the equation. -1L + -4l + -10lx + L + 5xL = 0 + L Reorder the terms: -1L + L + -4l + -10lx + 5xL = 0 + L Combine like terms: -1L + L = 0 0 + -4l + -10lx + 5xL = 0 + L -4l + -10lx + 5xL = 0 + L Remove the zero: -4l + -10lx + 5xL = L Add '4l' to each side of the equation. -4l + -10lx + 4l + 5xL = L + 4l Reorder the terms: -4l + 4l + -10lx + 5xL = L + 4l Combine like terms: -4l + 4l = 0 0 + -10lx + 5xL = L + 4l -10lx + 5xL = L + 4l Add '10lx' to each side of the equation. -10lx + 10lx + 5xL = L + 4l + 10lx Combine like terms: -10lx + 10lx = 0 0 + 5xL = L + 4l + 10lx 5xL = L + 4l + 10lx Add '-5xL' to each side of the equation. 5xL + -5xL = L + 4l + 10lx + -5xL Combine like terms: 5xL + -5xL = 0 0 = L + 4l + 10lx + -5xL Simplifying 0 = L + 4l + 10lx + -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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