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Simplifying 2Lnx = Ln(4x + 6) + -1Ln2 Reorder the terms: 2nxL = nL(6 + 4x) + -1Ln2 2nxL = (6 * nL + 4x * nL) + -1Ln2 2nxL = (6nL + 4nxL) + -1Ln2 Solving 2nxL = 6nL + 4nxL + -1n2L Solving for variable 'n'. Reorder the terms: -6nL + 2nxL + -4nxL + n2L = 6nL + 4nxL + -1n2L + -6nL + -4nxL + n2L Combine like terms: 2nxL + -4nxL = -2nxL -6nL + -2nxL + n2L = 6nL + 4nxL + -1n2L + -6nL + -4nxL + n2L Reorder the terms: -6nL + -2nxL + n2L = 6nL + -6nL + 4nxL + -4nxL + -1n2L + n2L Combine like terms: 6nL + -6nL = 0 -6nL + -2nxL + n2L = 0 + 4nxL + -4nxL + -1n2L + n2L -6nL + -2nxL + n2L = 4nxL + -4nxL + -1n2L + n2L Combine like terms: 4nxL + -4nxL = 0 -6nL + -2nxL + n2L = 0 + -1n2L + n2L -6nL + -2nxL + n2L = -1n2L + n2L Combine like terms: -1n2L + n2L = 0 -6nL + -2nxL + n2L = 0 Factor out the Greatest Common Factor (GCF), 'nL'. nL(-6 + -2x + n) = 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 '(-6 + -2x + n)' equal to zero and attempt to solve: Simplifying -6 + -2x + n = 0 Reorder the terms: -6 + n + -2x = 0 Solving -6 + n + -2x = 0 Move all terms containing n to the left, all other terms to the right. Add '6' to each side of the equation. -6 + n + 6 + -2x = 0 + 6 Reorder the terms: -6 + 6 + n + -2x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + n + -2x = 0 + 6 n + -2x = 0 + 6 Combine like terms: 0 + 6 = 6 n + -2x = 6 Add '2x' to each side of the equation. n + -2x + 2x = 6 + 2x Combine like terms: -2x + 2x = 0 n + 0 = 6 + 2x n = 6 + 2x Simplifying n = 6 + 2xSolution
n = {6 + 2x}
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