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Simplifying In(5x + 1) = In(3x + 7) Reorder the terms: nI(1 + 5x) = In(3x + 7) (1 * nI + 5x * nI) = In(3x + 7) (1nI + 5nxI) = In(3x + 7) Reorder the terms: 1nI + 5nxI = nI(7 + 3x) 1nI + 5nxI = (7 * nI + 3x * nI) 1nI + 5nxI = (7nI + 3nxI) Solving 1nI + 5nxI = 7nI + 3nxI Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-7nI' to each side of the equation. 1nI + -7nI + 5nxI = 7nI + -7nI + 3nxI Combine like terms: 1nI + -7nI = -6nI -6nI + 5nxI = 7nI + -7nI + 3nxI Combine like terms: 7nI + -7nI = 0 -6nI + 5nxI = 0 + 3nxI -6nI + 5nxI = 3nxI Add '-3nxI' to each side of the equation. -6nI + 5nxI + -3nxI = 3nxI + -3nxI Combine like terms: 5nxI + -3nxI = 2nxI -6nI + 2nxI = 3nxI + -3nxI Combine like terms: 3nxI + -3nxI = 0 -6nI + 2nxI = 0 Factor out the Greatest Common Factor (GCF), '2nI'. 2nI(-3 + x) = 0 Ignore the factor 2.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 '(-3 + x)' equal to zero and attempt to solve: Simplifying -3 + x = 0 Solving -3 + x = 0 Move all terms containing n to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + x = 0 + 3 x = 0 + 3 Combine like terms: 0 + 3 = 3 x = 3 Add '-1x' to each side of the equation. x + -1x = 3 + -1x Combine like terms: x + -1x = 0 0 = 3 + -1x Simplifying 0 = 3 + -1x 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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