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Simplifying In(4x + 1) = in(2x + 5) Reorder the terms: nI(1 + 4x) = in(2x + 5) (1 * nI + 4x * nI) = in(2x + 5) (1nI + 4nxI) = in(2x + 5) Reorder the terms: 1nI + 4nxI = in(5 + 2x) 1nI + 4nxI = (5 * in + 2x * in) 1nI + 4nxI = (5in + 2inx) Solving 1nI + 4nxI = 5in + 2inx Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-5in' to each side of the equation. 1nI + -5in + 4nxI = 5in + -5in + 2inx Reorder the terms: -5in + 1nI + 4nxI = 5in + -5in + 2inx Combine like terms: 5in + -5in = 0 -5in + 1nI + 4nxI = 0 + 2inx -5in + 1nI + 4nxI = 2inx Add '-2inx' to each side of the equation. -5in + 1nI + -2inx + 4nxI = 2inx + -2inx Reorder the terms: -5in + -2inx + 1nI + 4nxI = 2inx + -2inx Combine like terms: 2inx + -2inx = 0 -5in + -2inx + 1nI + 4nxI = 0 Factor out the Greatest Common Factor (GCF), 'n'. n(-5i + -2ix + I + 4xI) = 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 '(-5i + -2ix + I + 4xI)' equal to zero and attempt to solve: Simplifying -5i + -2ix + I + 4xI = 0 Reorder the terms: I + -5i + -2ix + 4xI = 0 Solving I + -5i + -2ix + 4xI = 0 Move all terms containing n to the left, all other terms to the right. Add '-1I' to each side of the equation. I + -5i + -2ix + -1I + 4xI = 0 + -1I Reorder the terms: I + -1I + -5i + -2ix + 4xI = 0 + -1I Combine like terms: I + -1I = 0 0 + -5i + -2ix + 4xI = 0 + -1I -5i + -2ix + 4xI = 0 + -1I Remove the zero: -5i + -2ix + 4xI = -1I Add '5i' to each side of the equation. -5i + -2ix + 5i + 4xI = -1I + 5i Reorder the terms: -5i + 5i + -2ix + 4xI = -1I + 5i Combine like terms: -5i + 5i = 0 0 + -2ix + 4xI = -1I + 5i -2ix + 4xI = -1I + 5i Add '2ix' to each side of the equation. -2ix + 2ix + 4xI = -1I + 5i + 2ix Combine like terms: -2ix + 2ix = 0 0 + 4xI = -1I + 5i + 2ix 4xI = -1I + 5i + 2ix Add '-4xI' to each side of the equation. 4xI + -4xI = -1I + 5i + 2ix + -4xI Combine like terms: 4xI + -4xI = 0 0 = -1I + 5i + 2ix + -4xI Simplifying 0 = -1I + 5i + 2ix + -4xI 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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