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Simplifying In(1 + y) + -1In(y) = In(x3 + 1) + -2In(x + -1) (1 * nI + y * nI) + -1In(y) = In(x3 + 1) + -2In(x + -1) (1nI + nyI) + -1In(y) = In(x3 + 1) + -2In(x + -1) Multiply nI * y 1nI + nyI + -1nyI = In(x3 + 1) + -2In(x + -1) Combine like terms: nyI + -1nyI = 0 1nI + 0 = In(x3 + 1) + -2In(x + -1) 1nI = In(x3 + 1) + -2In(x + -1) Reorder the terms: 1nI = nI(1 + x3) + -2In(x + -1) 1nI = (1 * nI + x3 * nI) + -2In(x + -1) 1nI = (1nI + nx3I) + -2In(x + -1) Reorder the terms: 1nI = 1nI + nx3I + -2nI(-1 + x) 1nI = 1nI + nx3I + (-1 * -2nI + x * -2nI) 1nI = 1nI + nx3I + (2nI + -2nxI) Reorder the terms: 1nI = 1nI + 2nI + -2nxI + nx3I Combine like terms: 1nI + 2nI = 3nI 1nI = 3nI + -2nxI + nx3I Solving 1nI = 3nI + -2nxI + nx3I Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-3nI' to each side of the equation. 1nI + -3nI = 3nI + -2nxI + -3nI + nx3I Combine like terms: 1nI + -3nI = -2nI -2nI = 3nI + -2nxI + -3nI + nx3I Reorder the terms: -2nI = 3nI + -3nI + -2nxI + nx3I Combine like terms: 3nI + -3nI = 0 -2nI = 0 + -2nxI + nx3I -2nI = -2nxI + nx3I Add '2nxI' to each side of the equation. -2nI + 2nxI = -2nxI + 2nxI + nx3I Combine like terms: -2nxI + 2nxI = 0 -2nI + 2nxI = 0 + nx3I -2nI + 2nxI = nx3I Add '-1nx3I' to each side of the equation. -2nI + 2nxI + -1nx3I = nx3I + -1nx3I Combine like terms: nx3I + -1nx3I = 0 -2nI + 2nxI + -1nx3I = 0 Factor out the Greatest Common Factor (GCF), 'nI'. nI(-2 + 2x + -1x3) = 0Subproblem 1
Set the factor 'nI' equal to zero and attempt to solve: Simplifying nI = 0 Solving nI = 0 Move all terms containing n to the left, all other terms to the right. Simplifying nI = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(-2 + 2x + -1x3)' equal to zero and attempt to solve: Simplifying -2 + 2x + -1x3 = 0 Solving -2 + 2x + -1x3 = 0 Move all terms containing n to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2x + 2 + -1x3 = 0 + 2 Reorder the terms: -2 + 2 + 2x + -1x3 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 2x + -1x3 = 0 + 2 2x + -1x3 = 0 + 2 Combine like terms: 0 + 2 = 2 2x + -1x3 = 2 Add '-2x' to each side of the equation. 2x + -2x + -1x3 = 2 + -2x Combine like terms: 2x + -2x = 0 0 + -1x3 = 2 + -2x -1x3 = 2 + -2x Add 'x3' to each side of the equation. -1x3 + x3 = 2 + -2x + x3 Combine like terms: -1x3 + x3 = 0 0 = 2 + -2x + x3 Simplifying 0 = 2 + -2x + x3 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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