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Simplifying Ln(x + 9) = ln(2x + -6) Reorder the terms: nL(9 + x) = ln(2x + -6) (9 * nL + x * nL) = ln(2x + -6) (9nL + nxL) = ln(2x + -6) Reorder the terms: 9nL + nxL = ln(-6 + 2x) 9nL + nxL = (-6 * ln + 2x * ln) 9nL + nxL = (-6ln + 2lnx) Solving 9nL + nxL = -6ln + 2lnx Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '6ln' to each side of the equation. 9nL + 6ln + nxL = -6ln + 6ln + 2lnx Reorder the terms: 6ln + 9nL + nxL = -6ln + 6ln + 2lnx Combine like terms: -6ln + 6ln = 0 6ln + 9nL + nxL = 0 + 2lnx 6ln + 9nL + nxL = 2lnx Add '-2lnx' to each side of the equation. 6ln + 9nL + -2lnx + nxL = 2lnx + -2lnx Reorder the terms: 6ln + -2lnx + 9nL + nxL = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 6ln + -2lnx + 9nL + nxL = 0 Factor out the Greatest Common Factor (GCF), 'n'. n(6l + -2lx + 9L + xL) = 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 '(6l + -2lx + 9L + xL)' equal to zero and attempt to solve: Simplifying 6l + -2lx + 9L + xL = 0 Reorder the terms: 9L + 6l + -2lx + xL = 0 Solving 9L + 6l + -2lx + xL = 0 Move all terms containing n to the left, all other terms to the right. Add '-9L' to each side of the equation. 9L + 6l + -2lx + -9L + xL = 0 + -9L Reorder the terms: 9L + -9L + 6l + -2lx + xL = 0 + -9L Combine like terms: 9L + -9L = 0 0 + 6l + -2lx + xL = 0 + -9L 6l + -2lx + xL = 0 + -9L Remove the zero: 6l + -2lx + xL = -9L Add '-6l' to each side of the equation. 6l + -2lx + -6l + xL = -9L + -6l Reorder the terms: 6l + -6l + -2lx + xL = -9L + -6l Combine like terms: 6l + -6l = 0 0 + -2lx + xL = -9L + -6l -2lx + xL = -9L + -6l Add '2lx' to each side of the equation. -2lx + 2lx + xL = -9L + -6l + 2lx Combine like terms: -2lx + 2lx = 0 0 + xL = -9L + -6l + 2lx xL = -9L + -6l + 2lx Add '-1xL' to each side of the equation. xL + -1xL = -9L + -6l + 2lx + -1xL Combine like terms: xL + -1xL = 0 0 = -9L + -6l + 2lx + -1xL Simplifying 0 = -9L + -6l + 2lx + -1xL 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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