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Simplifying 2Ln(x) + -1Ln(2x + -9) = Ln(7x) + -1Ln(x + -2) Multiply nL * x 2nxL + -1Ln(2x + -9) = Ln(7x) + -1Ln(x + -2) Reorder the terms: 2nxL + -1nL(-9 + 2x) = Ln(7x) + -1Ln(x + -2) 2nxL + (-9 * -1nL + 2x * -1nL) = Ln(7x) + -1Ln(x + -2) 2nxL + (9nL + -2nxL) = Ln(7x) + -1Ln(x + -2) Reorder the terms: 9nL + 2nxL + -2nxL = Ln(7x) + -1Ln(x + -2) Combine like terms: 2nxL + -2nxL = 0 9nL + 0 = Ln(7x) + -1Ln(x + -2) 9nL = Ln(7x) + -1Ln(x + -2) Remove parenthesis around (7x) 9nL = nL * 7x + -1Ln(x + -2) Reorder the terms for easier multiplication: 9nL = 7nL * x + -1Ln(x + -2) Multiply nL * x 9nL = 7nxL + -1Ln(x + -2) Reorder the terms: 9nL = 7nxL + -1nL(-2 + x) 9nL = 7nxL + (-2 * -1nL + x * -1nL) 9nL = 7nxL + (2nL + -1nxL) Reorder the terms: 9nL = 2nL + 7nxL + -1nxL Combine like terms: 7nxL + -1nxL = 6nxL 9nL = 2nL + 6nxL Solving 9nL = 2nL + 6nxL Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2nL' to each side of the equation. 9nL + -2nL = 2nL + -2nL + 6nxL Combine like terms: 9nL + -2nL = 7nL 7nL = 2nL + -2nL + 6nxL Combine like terms: 2nL + -2nL = 0 7nL = 0 + 6nxL 7nL = 6nxL Add '-6nxL' to each side of the equation. 7nL + -6nxL = 6nxL + -6nxL Combine like terms: 6nxL + -6nxL = 0 7nL + -6nxL = 0 Factor out the Greatest Common Factor (GCF), 'nL'. nL(7 + -6x) = 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 '(7 + -6x)' equal to zero and attempt to solve: Simplifying 7 + -6x = 0 Solving 7 + -6x = 0 Move all terms containing n to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -6x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -6x = 0 + -7 -6x = 0 + -7 Combine like terms: 0 + -7 = -7 -6x = -7 Add '6x' to each side of the equation. -6x + 6x = -7 + 6x Combine like terms: -6x + 6x = 0 0 = -7 + 6x Simplifying 0 = -7 + 6x 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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