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Simplifying Ln(x + 7) + -2Ln(x + 1) = Ln(16) Reorder the terms: nL(7 + x) + -2Ln(x + 1) = Ln(16) (7 * nL + x * nL) + -2Ln(x + 1) = Ln(16) (7nL + nxL) + -2Ln(x + 1) = Ln(16) Reorder the terms: 7nL + nxL + -2nL(1 + x) = Ln(16) 7nL + nxL + (1 * -2nL + x * -2nL) = Ln(16) 7nL + nxL + (-2nL + -2nxL) = Ln(16) Reorder the terms: 7nL + -2nL + nxL + -2nxL = Ln(16) Combine like terms: 7nL + -2nL = 5nL 5nL + nxL + -2nxL = Ln(16) Combine like terms: nxL + -2nxL = -1nxL 5nL + -1nxL = Ln(16) Reorder the terms for easier multiplication: 5nL + -1nxL = 16nL Solving 5nL + -1nxL = 16nL Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-16nL' to each side of the equation. 5nL + -16nL + -1nxL = 16nL + -16nL Combine like terms: 5nL + -16nL = -11nL -11nL + -1nxL = 16nL + -16nL Combine like terms: 16nL + -16nL = 0 -11nL + -1nxL = 0 Factor out the Greatest Common Factor (GCF), '-1nL'. -1nL(11 + x) = 0 Ignore the factor -1.Subproblem 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 '(11 + x)' equal to zero and attempt to solve: Simplifying 11 + x = 0 Solving 11 + x = 0 Move all terms containing n to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + x = 0 + -11 Combine like terms: 11 + -11 = 0 0 + x = 0 + -11 x = 0 + -11 Combine like terms: 0 + -11 = -11 x = -11 Add '-1x' to each side of the equation. x + -1x = -11 + -1x Combine like terms: x + -1x = 0 0 = -11 + -1x Simplifying 0 = -11 + -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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