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Simplifying In(x + -3) = In(5x) + In(2) Reorder the terms: nI(-3 + x) = In(5x) + In(2) (-3 * nI + x * nI) = In(5x) + In(2) (-3nI + nxI) = In(5x) + In(2) Remove parenthesis around (5x) -3nI + nxI = nI * 5x + In(2) Reorder the terms for easier multiplication: -3nI + nxI = 5nI * x + In(2) Multiply nI * x -3nI + nxI = 5nxI + In(2) Reorder the terms for easier multiplication: -3nI + nxI = 5nxI + 2nI Reorder the terms: -3nI + nxI = 2nI + 5nxI Solving -3nI + nxI = 2nI + 5nxI Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2nI' to each side of the equation. -3nI + -2nI + nxI = 2nI + -2nI + 5nxI Combine like terms: -3nI + -2nI = -5nI -5nI + nxI = 2nI + -2nI + 5nxI Combine like terms: 2nI + -2nI = 0 -5nI + nxI = 0 + 5nxI -5nI + nxI = 5nxI Add '-5nxI' to each side of the equation. -5nI + nxI + -5nxI = 5nxI + -5nxI Combine like terms: nxI + -5nxI = -4nxI -5nI + -4nxI = 5nxI + -5nxI Combine like terms: 5nxI + -5nxI = 0 -5nI + -4nxI = 0 Factor out the Greatest Common Factor (GCF), '-1nI'. -1nI(5 + 4x) = 0 Ignore the factor -1.Subproblem 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 '(5 + 4x)' equal to zero and attempt to solve: Simplifying 5 + 4x = 0 Solving 5 + 4x = 0 Move all terms containing n to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 4x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 4x = 0 + -5 4x = 0 + -5 Combine like terms: 0 + -5 = -5 4x = -5 Add '-4x' to each side of the equation. 4x + -4x = -5 + -4x Combine like terms: 4x + -4x = 0 0 = -5 + -4x Simplifying 0 = -5 + -4x 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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