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Simplifying 2Lnx = Ln(4x + 6) + -2Ln Reorder the terms: 2nxL = nL(6 + 4x) + -2Ln 2nxL = (6 * nL + 4x * nL) + -2Ln 2nxL = (6nL + 4nxL) + -2Ln Reorder the terms: 2nxL = 6nL + -2nL + 4nxL Combine like terms: 6nL + -2nL = 4nL 2nxL = 4nL + 4nxL Solving 2nxL = 4nL + 4nxL Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-4nL' to each side of the equation. -4nL + 2nxL = 4nL + -4nL + 4nxL Combine like terms: 4nL + -4nL = 0 -4nL + 2nxL = 0 + 4nxL -4nL + 2nxL = 4nxL Add '-4nxL' to each side of the equation. -4nL + 2nxL + -4nxL = 4nxL + -4nxL Combine like terms: 2nxL + -4nxL = -2nxL -4nL + -2nxL = 4nxL + -4nxL Combine like terms: 4nxL + -4nxL = 0 -4nL + -2nxL = 0 Factor out the Greatest Common Factor (GCF), '-2nL'. -2nL(2 + x) = 0 Ignore the factor -2.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 '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 0 Move all terms containing n to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Add '-1x' to each side of the equation. x + -1x = -2 + -1x Combine like terms: x + -1x = 0 0 = -2 + -1x Simplifying 0 = -2 + -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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