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Simplifying Ln(5x + -7) = ln(4x + 5) Reorder the terms: nL(-7 + 5x) = ln(4x + 5) (-7 * nL + 5x * nL) = ln(4x + 5) (-7nL + 5nxL) = ln(4x + 5) Reorder the terms: -7nL + 5nxL = ln(5 + 4x) -7nL + 5nxL = (5 * ln + 4x * ln) -7nL + 5nxL = (5ln + 4lnx) Solving -7nL + 5nxL = 5ln + 4lnx Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-5ln' to each side of the equation. -7nL + -5ln + 5nxL = 5ln + -5ln + 4lnx Reorder the terms: -5ln + -7nL + 5nxL = 5ln + -5ln + 4lnx Combine like terms: 5ln + -5ln = 0 -5ln + -7nL + 5nxL = 0 + 4lnx -5ln + -7nL + 5nxL = 4lnx Add '-4lnx' to each side of the equation. -5ln + -7nL + -4lnx + 5nxL = 4lnx + -4lnx Reorder the terms: -5ln + -4lnx + -7nL + 5nxL = 4lnx + -4lnx Combine like terms: 4lnx + -4lnx = 0 -5ln + -4lnx + -7nL + 5nxL = 0 Factor out the Greatest Common Factor (GCF), 'n'. n(-5l + -4lx + -7L + 5xL) = 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 '(-5l + -4lx + -7L + 5xL)' equal to zero and attempt to solve: Simplifying -5l + -4lx + -7L + 5xL = 0 Reorder the terms: -7L + -5l + -4lx + 5xL = 0 Solving -7L + -5l + -4lx + 5xL = 0 Move all terms containing n to the left, all other terms to the right. Add '7L' to each side of the equation. -7L + -5l + -4lx + 7L + 5xL = 0 + 7L Reorder the terms: -7L + 7L + -5l + -4lx + 5xL = 0 + 7L Combine like terms: -7L + 7L = 0 0 + -5l + -4lx + 5xL = 0 + 7L -5l + -4lx + 5xL = 0 + 7L Remove the zero: -5l + -4lx + 5xL = 7L Add '5l' to each side of the equation. -5l + -4lx + 5l + 5xL = 7L + 5l Reorder the terms: -5l + 5l + -4lx + 5xL = 7L + 5l Combine like terms: -5l + 5l = 0 0 + -4lx + 5xL = 7L + 5l -4lx + 5xL = 7L + 5l Add '4lx' to each side of the equation. -4lx + 4lx + 5xL = 7L + 5l + 4lx Combine like terms: -4lx + 4lx = 0 0 + 5xL = 7L + 5l + 4lx 5xL = 7L + 5l + 4lx Add '-5xL' to each side of the equation. 5xL + -5xL = 7L + 5l + 4lx + -5xL Combine like terms: 5xL + -5xL = 0 0 = 7L + 5l + 4lx + -5xL Simplifying 0 = 7L + 5l + 4lx + -5xL 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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