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Simplifying Ln(x + 5) + Lnx = Ln(x + 21) Reorder the terms: nL(5 + x) + Lnx = Ln(x + 21) (5 * nL + x * nL) + Lnx = Ln(x + 21) (5nL + nxL) + Lnx = Ln(x + 21) Combine like terms: nxL + nxL = 2nxL 5nL + 2nxL = Ln(x + 21) Reorder the terms: 5nL + 2nxL = nL(21 + x) 5nL + 2nxL = (21 * nL + x * nL) 5nL + 2nxL = (21nL + nxL) Solving 5nL + 2nxL = 21nL + nxL Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-21nL' to each side of the equation. 5nL + -21nL + 2nxL = 21nL + -21nL + nxL Combine like terms: 5nL + -21nL = -16nL -16nL + 2nxL = 21nL + -21nL + nxL Combine like terms: 21nL + -21nL = 0 -16nL + 2nxL = 0 + nxL -16nL + 2nxL = nxL Add '-1nxL' to each side of the equation. -16nL + 2nxL + -1nxL = nxL + -1nxL Combine like terms: 2nxL + -1nxL = 1nxL -16nL + 1nxL = nxL + -1nxL Combine like terms: nxL + -1nxL = 0 -16nL + 1nxL = 0 Factor out the Greatest Common Factor (GCF), 'nL'. nL(-16 + x) = 0Subproblem 1
Set the factor 'nL' equal to zero and attempt to solve: Simplifying nL = 0 Solving nL = 0 Move all terms containing n to the left, all other terms to the right. Simplifying nL = 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 '(-16 + x)' equal to zero and attempt to solve: Simplifying -16 + x = 0 Solving -16 + x = 0 Move all terms containing n to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + x = 0 + 16 Combine like terms: -16 + 16 = 0 0 + x = 0 + 16 x = 0 + 16 Combine like terms: 0 + 16 = 16 x = 16 Add '-1x' to each side of the equation. x + -1x = 16 + -1x Combine like terms: x + -1x = 0 0 = 16 + -1x Simplifying 0 = 16 + -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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