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Simplifying Ln(5x + -6) = ln(3 + -1x) Reorder the terms: nL(-6 + 5x) = ln(3 + -1x) (-6 * nL + 5x * nL) = ln(3 + -1x) (-6nL + 5nxL) = ln(3 + -1x) -6nL + 5nxL = (3 * ln + -1x * ln) -6nL + 5nxL = (3ln + -1lnx) Solving -6nL + 5nxL = 3ln + -1lnx Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-3ln' to each side of the equation. -6nL + -3ln + 5nxL = 3ln + -3ln + -1lnx Reorder the terms: -3ln + -6nL + 5nxL = 3ln + -3ln + -1lnx Combine like terms: 3ln + -3ln = 0 -3ln + -6nL + 5nxL = 0 + -1lnx -3ln + -6nL + 5nxL = -1lnx Add 'lnx' to each side of the equation. -3ln + -6nL + lnx + 5nxL = -1lnx + lnx Reorder the terms: -3ln + lnx + -6nL + 5nxL = -1lnx + lnx Combine like terms: -1lnx + lnx = 0 -3ln + lnx + -6nL + 5nxL = 0 Factor out the Greatest Common Factor (GCF), 'n'. n(-3l + lx + -6L + 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 '(-3l + lx + -6L + 5xL)' equal to zero and attempt to solve: Simplifying -3l + lx + -6L + 5xL = 0 Reorder the terms: -6L + -3l + lx + 5xL = 0 Solving -6L + -3l + lx + 5xL = 0 Move all terms containing n to the left, all other terms to the right. Add '6L' to each side of the equation. -6L + -3l + lx + 6L + 5xL = 0 + 6L Reorder the terms: -6L + 6L + -3l + lx + 5xL = 0 + 6L Combine like terms: -6L + 6L = 0 0 + -3l + lx + 5xL = 0 + 6L -3l + lx + 5xL = 0 + 6L Remove the zero: -3l + lx + 5xL = 6L Add '3l' to each side of the equation. -3l + lx + 3l + 5xL = 6L + 3l Reorder the terms: -3l + 3l + lx + 5xL = 6L + 3l Combine like terms: -3l + 3l = 0 0 + lx + 5xL = 6L + 3l lx + 5xL = 6L + 3l Add '-1lx' to each side of the equation. lx + -1lx + 5xL = 6L + 3l + -1lx Combine like terms: lx + -1lx = 0 0 + 5xL = 6L + 3l + -1lx 5xL = 6L + 3l + -1lx Add '-5xL' to each side of the equation. 5xL + -5xL = 6L + 3l + -1lx + -5xL Combine like terms: 5xL + -5xL = 0 0 = 6L + 3l + -1lx + -5xL Simplifying 0 = 6L + 3l + -1lx + -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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