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Simplifying In(5x + 7) = In(2x + 43) Reorder the terms: nI(7 + 5x) = In(2x + 43) (7 * nI + 5x * nI) = In(2x + 43) (7nI + 5nxI) = In(2x + 43) Reorder the terms: 7nI + 5nxI = nI(43 + 2x) 7nI + 5nxI = (43 * nI + 2x * nI) 7nI + 5nxI = (43nI + 2nxI) Solving 7nI + 5nxI = 43nI + 2nxI Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-43nI' to each side of the equation. 7nI + -43nI + 5nxI = 43nI + -43nI + 2nxI Combine like terms: 7nI + -43nI = -36nI -36nI + 5nxI = 43nI + -43nI + 2nxI Combine like terms: 43nI + -43nI = 0 -36nI + 5nxI = 0 + 2nxI -36nI + 5nxI = 2nxI Add '-2nxI' to each side of the equation. -36nI + 5nxI + -2nxI = 2nxI + -2nxI Combine like terms: 5nxI + -2nxI = 3nxI -36nI + 3nxI = 2nxI + -2nxI Combine like terms: 2nxI + -2nxI = 0 -36nI + 3nxI = 0 Factor out the Greatest Common Factor (GCF), '3nI'. 3nI(-12 + x) = 0 Ignore the factor 3.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 '(-12 + x)' equal to zero and attempt to solve: Simplifying -12 + x = 0 Solving -12 + x = 0 Move all terms containing n to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = 0 + 12 Combine like terms: -12 + 12 = 0 0 + x = 0 + 12 x = 0 + 12 Combine like terms: 0 + 12 = 12 x = 12 Add '-1x' to each side of the equation. x + -1x = 12 + -1x Combine like terms: x + -1x = 0 0 = 12 + -1x Simplifying 0 = 12 + -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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