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Simplifying Ln(x + 1) = Ln(3x + 8) + -1lnx Reorder the terms: nL(1 + x) = Ln(3x + 8) + -1lnx (1 * nL + x * nL) = Ln(3x + 8) + -1lnx (1nL + nxL) = Ln(3x + 8) + -1lnx Reorder the terms: 1nL + nxL = nL(8 + 3x) + -1lnx 1nL + nxL = (8 * nL + 3x * nL) + -1lnx 1nL + nxL = (8nL + 3nxL) + -1lnx Reorder the terms: 1nL + nxL = -1lnx + 8nL + 3nxL Solving 1nL + nxL = -1lnx + 8nL + 3nxL Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add 'lnx' to each side of the equation. 1nL + lnx + nxL = -1lnx + 8nL + lnx + 3nxL Reorder the terms: lnx + 1nL + nxL = -1lnx + 8nL + lnx + 3nxL Reorder the terms: lnx + 1nL + nxL = -1lnx + lnx + 8nL + 3nxL Combine like terms: -1lnx + lnx = 0 lnx + 1nL + nxL = 0 + 8nL + 3nxL lnx + 1nL + nxL = 8nL + 3nxL Add '-8nL' to each side of the equation. lnx + 1nL + -8nL + nxL = 8nL + -8nL + 3nxL Combine like terms: 1nL + -8nL = -7nL lnx + -7nL + nxL = 8nL + -8nL + 3nxL Combine like terms: 8nL + -8nL = 0 lnx + -7nL + nxL = 0 + 3nxL lnx + -7nL + nxL = 3nxL Add '-3nxL' to each side of the equation. lnx + -7nL + nxL + -3nxL = 3nxL + -3nxL Combine like terms: nxL + -3nxL = -2nxL lnx + -7nL + -2nxL = 3nxL + -3nxL Combine like terms: 3nxL + -3nxL = 0 lnx + -7nL + -2nxL = 0 Factor out the Greatest Common Factor (GCF), 'n'. n(lx + -7L + -2xL) = 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 '(lx + -7L + -2xL)' equal to zero and attempt to solve: Simplifying lx + -7L + -2xL = 0 Reorder the terms: -7L + lx + -2xL = 0 Solving -7L + lx + -2xL = 0 Move all terms containing n to the left, all other terms to the right. Add '7L' to each side of the equation. -7L + lx + 7L + -2xL = 0 + 7L Reorder the terms: -7L + 7L + lx + -2xL = 0 + 7L Combine like terms: -7L + 7L = 0 0 + lx + -2xL = 0 + 7L lx + -2xL = 0 + 7L Remove the zero: lx + -2xL = 7L Add '-1lx' to each side of the equation. lx + -1lx + -2xL = 7L + -1lx Combine like terms: lx + -1lx = 0 0 + -2xL = 7L + -1lx -2xL = 7L + -1lx Add '2xL' to each side of the equation. -2xL + 2xL = 7L + -1lx + 2xL Combine like terms: -2xL + 2xL = 0 0 = 7L + -1lx + 2xL Simplifying 0 = 7L + -1lx + 2xL 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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