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Simplifying Ln(6x + 5) = ln(5x + -4) Reorder the terms: nL(5 + 6x) = ln(5x + -4) (5 * nL + 6x * nL) = ln(5x + -4) (5nL + 6nxL) = ln(5x + -4) Reorder the terms: 5nL + 6nxL = ln(-4 + 5x) 5nL + 6nxL = (-4 * ln + 5x * ln) 5nL + 6nxL = (-4ln + 5lnx) Solving 5nL + 6nxL = -4ln + 5lnx Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '4ln' to each side of the equation. 5nL + 4ln + 6nxL = -4ln + 4ln + 5lnx Reorder the terms: 4ln + 5nL + 6nxL = -4ln + 4ln + 5lnx Combine like terms: -4ln + 4ln = 0 4ln + 5nL + 6nxL = 0 + 5lnx 4ln + 5nL + 6nxL = 5lnx Add '-5lnx' to each side of the equation. 4ln + 5nL + -5lnx + 6nxL = 5lnx + -5lnx Reorder the terms: 4ln + -5lnx + 5nL + 6nxL = 5lnx + -5lnx Combine like terms: 5lnx + -5lnx = 0 4ln + -5lnx + 5nL + 6nxL = 0 Factor out the Greatest Common Factor (GCF), 'n'. n(4l + -5lx + 5L + 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 '(4l + -5lx + 5L + 6xL)' equal to zero and attempt to solve: Simplifying 4l + -5lx + 5L + 6xL = 0 Reorder the terms: 5L + 4l + -5lx + 6xL = 0 Solving 5L + 4l + -5lx + 6xL = 0 Move all terms containing n to the left, all other terms to the right. Add '-5L' to each side of the equation. 5L + 4l + -5lx + -5L + 6xL = 0 + -5L Reorder the terms: 5L + -5L + 4l + -5lx + 6xL = 0 + -5L Combine like terms: 5L + -5L = 0 0 + 4l + -5lx + 6xL = 0 + -5L 4l + -5lx + 6xL = 0 + -5L Remove the zero: 4l + -5lx + 6xL = -5L Add '-4l' to each side of the equation. 4l + -5lx + -4l + 6xL = -5L + -4l Reorder the terms: 4l + -4l + -5lx + 6xL = -5L + -4l Combine like terms: 4l + -4l = 0 0 + -5lx + 6xL = -5L + -4l -5lx + 6xL = -5L + -4l Add '5lx' to each side of the equation. -5lx + 5lx + 6xL = -5L + -4l + 5lx Combine like terms: -5lx + 5lx = 0 0 + 6xL = -5L + -4l + 5lx 6xL = -5L + -4l + 5lx Add '-6xL' to each side of the equation. 6xL + -6xL = -5L + -4l + 5lx + -6xL Combine like terms: 6xL + -6xL = 0 0 = -5L + -4l + 5lx + -6xL Simplifying 0 = -5L + -4l + 5lx + -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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