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Simplifying Ln(9 + -1x2) + Ln(x + 3) = 3Ln * 3 (9 * nL + -1x2 * nL) + Ln(x + 3) = 3Ln * 3 (9nL + -1nx2L) + Ln(x + 3) = 3Ln * 3 Reorder the terms: 9nL + -1nx2L + nL(3 + x) = 3Ln * 3 9nL + -1nx2L + (3 * nL + x * nL) = 3Ln * 3 9nL + -1nx2L + (3nL + nxL) = 3Ln * 3 Reorder the terms: 9nL + 3nL + nxL + -1nx2L = 3Ln * 3 Combine like terms: 9nL + 3nL = 12nL 12nL + nxL + -1nx2L = 3Ln * 3 Reorder the terms for easier multiplication: 12nL + nxL + -1nx2L = 3 * 3nL Multiply 3 * 3 12nL + nxL + -1nx2L = 9nL Solving 12nL + nxL + -1nx2L = 9nL Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-9nL' to each side of the equation. 12nL + nxL + -9nL + -1nx2L = 9nL + -9nL Reorder the terms: 12nL + -9nL + nxL + -1nx2L = 9nL + -9nL Combine like terms: 12nL + -9nL = 3nL 3nL + nxL + -1nx2L = 9nL + -9nL Combine like terms: 9nL + -9nL = 0 3nL + nxL + -1nx2L = 0 Factor out the Greatest Common Factor (GCF), 'nL'. nL(3 + x + -1x2) = 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 '(3 + x + -1x2)' equal to zero and attempt to solve: Simplifying 3 + x + -1x2 = 0 Solving 3 + x + -1x2 = 0 Move all terms containing n to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + x + -3 + -1x2 = 0 + -3 Reorder the terms: 3 + -3 + x + -1x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x + -1x2 = 0 + -3 x + -1x2 = 0 + -3 Combine like terms: 0 + -3 = -3 x + -1x2 = -3 Add '-1x' to each side of the equation. x + -1x + -1x2 = -3 + -1x Combine like terms: x + -1x = 0 0 + -1x2 = -3 + -1x -1x2 = -3 + -1x Add 'x2' to each side of the equation. -1x2 + x2 = -3 + -1x + x2 Combine like terms: -1x2 + x2 = 0 0 = -3 + -1x + x2 Simplifying 0 = -3 + -1x + x2 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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