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Simplifying Ln(6 + -1x) = ln(15 + -2x) (6 * nL + -1x * nL) = ln(15 + -2x) (6nL + -1nxL) = ln(15 + -2x) 6nL + -1nxL = (15 * ln + -2x * ln) 6nL + -1nxL = (15ln + -2lnx) Solving 6nL + -1nxL = 15ln + -2lnx Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-15ln' to each side of the equation. 6nL + -15ln + -1nxL = 15ln + -15ln + -2lnx Reorder the terms: -15ln + 6nL + -1nxL = 15ln + -15ln + -2lnx Combine like terms: 15ln + -15ln = 0 -15ln + 6nL + -1nxL = 0 + -2lnx -15ln + 6nL + -1nxL = -2lnx Add '2lnx' to each side of the equation. -15ln + 6nL + 2lnx + -1nxL = -2lnx + 2lnx Reorder the terms: -15ln + 2lnx + 6nL + -1nxL = -2lnx + 2lnx Combine like terms: -2lnx + 2lnx = 0 -15ln + 2lnx + 6nL + -1nxL = 0 Factor out the Greatest Common Factor (GCF), 'n'. n(-15l + 2lx + 6L + -1xL) = 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 '(-15l + 2lx + 6L + -1xL)' equal to zero and attempt to solve: Simplifying -15l + 2lx + 6L + -1xL = 0 Reorder the terms: 6L + -15l + 2lx + -1xL = 0 Solving 6L + -15l + 2lx + -1xL = 0 Move all terms containing n to the left, all other terms to the right. Add '-6L' to each side of the equation. 6L + -15l + 2lx + -6L + -1xL = 0 + -6L Reorder the terms: 6L + -6L + -15l + 2lx + -1xL = 0 + -6L Combine like terms: 6L + -6L = 0 0 + -15l + 2lx + -1xL = 0 + -6L -15l + 2lx + -1xL = 0 + -6L Remove the zero: -15l + 2lx + -1xL = -6L Add '15l' to each side of the equation. -15l + 2lx + 15l + -1xL = -6L + 15l Reorder the terms: -15l + 15l + 2lx + -1xL = -6L + 15l Combine like terms: -15l + 15l = 0 0 + 2lx + -1xL = -6L + 15l 2lx + -1xL = -6L + 15l Add '-2lx' to each side of the equation. 2lx + -2lx + -1xL = -6L + 15l + -2lx Combine like terms: 2lx + -2lx = 0 0 + -1xL = -6L + 15l + -2lx -1xL = -6L + 15l + -2lx Add 'xL' to each side of the equation. -1xL + xL = -6L + 15l + -2lx + xL Combine like terms: -1xL + xL = 0 0 = -6L + 15l + -2lx + xL Simplifying 0 = -6L + 15l + -2lx + xL 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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