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Simplifying In(x + 5) = ln(x + 8) + -1ln(x + 4) Reorder the terms: nI(5 + x) = ln(x + 8) + -1ln(x + 4) (5 * nI + x * nI) = ln(x + 8) + -1ln(x + 4) (5nI + nxI) = ln(x + 8) + -1ln(x + 4) Reorder the terms: 5nI + nxI = ln(8 + x) + -1ln(x + 4) 5nI + nxI = (8 * ln + x * ln) + -1ln(x + 4) 5nI + nxI = (8ln + lnx) + -1ln(x + 4) Reorder the terms: 5nI + nxI = 8ln + lnx + -1ln(4 + x) 5nI + nxI = 8ln + lnx + (4 * -1ln + x * -1ln) 5nI + nxI = 8ln + lnx + (-4ln + -1lnx) Reorder the terms: 5nI + nxI = 8ln + -4ln + lnx + -1lnx Combine like terms: 8ln + -4ln = 4ln 5nI + nxI = 4ln + lnx + -1lnx Combine like terms: lnx + -1lnx = 0 5nI + nxI = 4ln + 0 5nI + nxI = 4ln Solving 5nI + nxI = 4ln Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-4ln' to each side of the equation. 5nI + -4ln + nxI = 4ln + -4ln Reorder the terms: -4ln + 5nI + nxI = 4ln + -4ln Combine like terms: 4ln + -4ln = 0 -4ln + 5nI + nxI = 0 Factor out the Greatest Common Factor (GCF), 'n'. n(-4l + 5I + xI) = 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 '(-4l + 5I + xI)' equal to zero and attempt to solve: Simplifying -4l + 5I + xI = 0 Reorder the terms: 5I + -4l + xI = 0 Solving 5I + -4l + xI = 0 Move all terms containing n to the left, all other terms to the right. Add '-5I' to each side of the equation. 5I + -4l + -5I + xI = 0 + -5I Reorder the terms: 5I + -5I + -4l + xI = 0 + -5I Combine like terms: 5I + -5I = 0 0 + -4l + xI = 0 + -5I -4l + xI = 0 + -5I Remove the zero: -4l + xI = -5I Add '4l' to each side of the equation. -4l + 4l + xI = -5I + 4l Combine like terms: -4l + 4l = 0 0 + xI = -5I + 4l xI = -5I + 4l Add '-1xI' to each side of the equation. xI + -1xI = -5I + 4l + -1xI Combine like terms: xI + -1xI = 0 0 = -5I + 4l + -1xI Simplifying 0 = -5I + 4l + -1xI 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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