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Simplifying Ln(8 + x) = lnx + ln(x + -1) (8 * nL + x * nL) = lnx + ln(x + -1) (8nL + nxL) = lnx + ln(x + -1) Reorder the terms: 8nL + nxL = lnx + ln(-1 + x) 8nL + nxL = lnx + (-1 * ln + x * ln) 8nL + nxL = lnx + (-1ln + lnx) Reorder the terms: 8nL + nxL = -1ln + lnx + lnx Combine like terms: lnx + lnx = 2lnx 8nL + nxL = -1ln + 2lnx Solving 8nL + nxL = -1ln + 2lnx Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add 'ln' to each side of the equation. 8nL + ln + nxL = -1ln + ln + 2lnx Reorder the terms: ln + 8nL + nxL = -1ln + ln + 2lnx Combine like terms: -1ln + ln = 0 ln + 8nL + nxL = 0 + 2lnx ln + 8nL + nxL = 2lnx Add '-2lnx' to each side of the equation. ln + 8nL + -2lnx + nxL = 2lnx + -2lnx Reorder the terms: ln + -2lnx + 8nL + nxL = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 ln + -2lnx + 8nL + nxL = 0 Factor out the Greatest Common Factor (GCF), 'n'. n(l + -2lx + 8L + 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 '(l + -2lx + 8L + xL)' equal to zero and attempt to solve: Simplifying l + -2lx + 8L + xL = 0 Reorder the terms: 8L + l + -2lx + xL = 0 Solving 8L + l + -2lx + xL = 0 Move all terms containing n to the left, all other terms to the right. Add '-8L' to each side of the equation. 8L + l + -2lx + -8L + xL = 0 + -8L Reorder the terms: 8L + -8L + l + -2lx + xL = 0 + -8L Combine like terms: 8L + -8L = 0 0 + l + -2lx + xL = 0 + -8L l + -2lx + xL = 0 + -8L Remove the zero: l + -2lx + xL = -8L Add '-1l' to each side of the equation. l + -2lx + -1l + xL = -8L + -1l Reorder the terms: l + -1l + -2lx + xL = -8L + -1l Combine like terms: l + -1l = 0 0 + -2lx + xL = -8L + -1l -2lx + xL = -8L + -1l Add '2lx' to each side of the equation. -2lx + 2lx + xL = -8L + -1l + 2lx Combine like terms: -2lx + 2lx = 0 0 + xL = -8L + -1l + 2lx xL = -8L + -1l + 2lx Add '-1xL' to each side of the equation. xL + -1xL = -8L + -1l + 2lx + -1xL Combine like terms: xL + -1xL = 0 0 = -8L + -1l + 2lx + -1xL Simplifying 0 = -8L + -1l + 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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