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