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Simplifying Ln(6x + -15) = ln(41 + -2x) Reorder the terms: nL(-15 + 6x) = ln(41 + -2x) (-15 * nL + 6x * nL) = ln(41 + -2x) (-15nL + 6nxL) = ln(41 + -2x) -15nL + 6nxL = (41 * ln + -2x * ln) -15nL + 6nxL = (41ln + -2lnx) Solving -15nL + 6nxL = 41ln + -2lnx Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-41ln' to each side of the equation. -15nL + -41ln + 6nxL = 41ln + -41ln + -2lnx Reorder the terms: -41ln + -15nL + 6nxL = 41ln + -41ln + -2lnx Combine like terms: 41ln + -41ln = 0 -41ln + -15nL + 6nxL = 0 + -2lnx -41ln + -15nL + 6nxL = -2lnx Add '2lnx' to each side of the equation. -41ln + -15nL + 2lnx + 6nxL = -2lnx + 2lnx Reorder the terms: -41ln + 2lnx + -15nL + 6nxL = -2lnx + 2lnx Combine like terms: -2lnx + 2lnx = 0 -41ln + 2lnx + -15nL + 6nxL = 0 Factor out the Greatest Common Factor (GCF), 'n'. n(-41l + 2lx + -15L + 6xL) = 0Subproblem 1
Set the factor 'n' equal to zero and attempt to solve: Simplifying n = 0 Solving n = 0 Move all terms containing n to the left, all other terms to the right. Simplifying n = 0Subproblem 2
Set the factor '(-41l + 2lx + -15L + 6xL)' equal to zero and attempt to solve: Simplifying -41l + 2lx + -15L + 6xL = 0 Reorder the terms: -15L + -41l + 2lx + 6xL = 0 Solving -15L + -41l + 2lx + 6xL = 0 Move all terms containing n to the left, all other terms to the right. Add '15L' to each side of the equation. -15L + -41l + 2lx + 15L + 6xL = 0 + 15L Reorder the terms: -15L + 15L + -41l + 2lx + 6xL = 0 + 15L Combine like terms: -15L + 15L = 0 0 + -41l + 2lx + 6xL = 0 + 15L -41l + 2lx + 6xL = 0 + 15L Remove the zero: -41l + 2lx + 6xL = 15L Add '41l' to each side of the equation. -41l + 2lx + 41l + 6xL = 15L + 41l Reorder the terms: -41l + 41l + 2lx + 6xL = 15L + 41l Combine like terms: -41l + 41l = 0 0 + 2lx + 6xL = 15L + 41l 2lx + 6xL = 15L + 41l Add '-2lx' to each side of the equation. 2lx + -2lx + 6xL = 15L + 41l + -2lx Combine like terms: 2lx + -2lx = 0 0 + 6xL = 15L + 41l + -2lx 6xL = 15L + 41l + -2lx Add '-6xL' to each side of the equation. 6xL + -6xL = 15L + 41l + -2lx + -6xL Combine like terms: 6xL + -6xL = 0 0 = 15L + 41l + -2lx + -6xL Simplifying 0 = 15L + 41l + -2lx + -6xL The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
n = {0}
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