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Simplifying Ln(x + 7) = ln(3x + -5) Reorder the terms: nL(7 + x) = ln(3x + -5) (7 * nL + x * nL) = ln(3x + -5) (7nL + nxL) = ln(3x + -5) Reorder the terms: 7nL + nxL = ln(-5 + 3x) 7nL + nxL = (-5 * ln + 3x * ln) 7nL + nxL = (-5ln + 3lnx) Solving 7nL + nxL = -5ln + 3lnx 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 + nxL = -5ln + 5ln + 3lnx Reorder the terms: 5ln + 7nL + nxL = -5ln + 5ln + 3lnx Combine like terms: -5ln + 5ln = 0 5ln + 7nL + nxL = 0 + 3lnx 5ln + 7nL + nxL = 3lnx Add '-3lnx' to each side of the equation. 5ln + 7nL + -3lnx + nxL = 3lnx + -3lnx Reorder the terms: 5ln + -3lnx + 7nL + nxL = 3lnx + -3lnx Combine like terms: 3lnx + -3lnx = 0 5ln + -3lnx + 7nL + nxL = 0 Factor out the Greatest Common Factor (GCF), 'n'. n(5l + -3lx + 7L + xL) = 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 + -3lx + 7L + xL)' equal to zero and attempt to solve: Simplifying 5l + -3lx + 7L + xL = 0 Reorder the terms: 7L + 5l + -3lx + xL = 0 Solving 7L + 5l + -3lx + xL = 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 + -3lx + -7L + xL = 0 + -7L Reorder the terms: 7L + -7L + 5l + -3lx + xL = 0 + -7L Combine like terms: 7L + -7L = 0 0 + 5l + -3lx + xL = 0 + -7L 5l + -3lx + xL = 0 + -7L Remove the zero: 5l + -3lx + xL = -7L Add '-5l' to each side of the equation. 5l + -3lx + -5l + xL = -7L + -5l Reorder the terms: 5l + -5l + -3lx + xL = -7L + -5l Combine like terms: 5l + -5l = 0 0 + -3lx + xL = -7L + -5l -3lx + xL = -7L + -5l Add '3lx' to each side of the equation. -3lx + 3lx + xL = -7L + -5l + 3lx Combine like terms: -3lx + 3lx = 0 0 + xL = -7L + -5l + 3lx xL = -7L + -5l + 3lx Add '-1xL' to each side of the equation. xL + -1xL = -7L + -5l + 3lx + -1xL Combine like terms: xL + -1xL = 0 0 = -7L + -5l + 3lx + -1xL Simplifying 0 = -7L + -5l + 3lx + -1xL 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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