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