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Simplifying Ln(x + 7) = 2ln(3) + -1ln(x + -7) Reorder the terms: nL(7 + x) = 2ln(3) + -1ln(x + -7) (7 * nL + x * nL) = 2ln(3) + -1ln(x + -7) (7nL + nxL) = 2ln(3) + -1ln(x + -7) Reorder the terms for easier multiplication: 7nL + nxL = 2 * 3ln + -1ln(x + -7) Multiply 2 * 3 7nL + nxL = 6ln + -1ln(x + -7) Reorder the terms: 7nL + nxL = 6ln + -1ln(-7 + x) 7nL + nxL = 6ln + (-7 * -1ln + x * -1ln) 7nL + nxL = 6ln + (7ln + -1lnx) Combine like terms: 6ln + 7ln = 13ln 7nL + nxL = 13ln + -1lnx Solving 7nL + nxL = 13ln + -1lnx Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-13ln' to each side of the equation. 7nL + -13ln + nxL = 13ln + -13ln + -1lnx Reorder the terms: -13ln + 7nL + nxL = 13ln + -13ln + -1lnx Combine like terms: 13ln + -13ln = 0 -13ln + 7nL + nxL = 0 + -1lnx -13ln + 7nL + nxL = -1lnx Add 'lnx' to each side of the equation. -13ln + 7nL + lnx + nxL = -1lnx + lnx Reorder the terms: -13ln + lnx + 7nL + nxL = -1lnx + lnx Combine like terms: -1lnx + lnx = 0 -13ln + lnx + 7nL + nxL = 0 Factor out the Greatest Common Factor (GCF), 'n'. n(-13l + lx + 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 '(-13l + lx + 7L + xL)' equal to zero and attempt to solve: Simplifying -13l + lx + 7L + xL = 0 Reorder the terms: 7L + -13l + lx + xL = 0 Solving 7L + -13l + lx + 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 + -13l + lx + -7L + xL = 0 + -7L Reorder the terms: 7L + -7L + -13l + lx + xL = 0 + -7L Combine like terms: 7L + -7L = 0 0 + -13l + lx + xL = 0 + -7L -13l + lx + xL = 0 + -7L Remove the zero: -13l + lx + xL = -7L Add '13l' to each side of the equation. -13l + lx + 13l + xL = -7L + 13l Reorder the terms: -13l + 13l + lx + xL = -7L + 13l Combine like terms: -13l + 13l = 0 0 + lx + xL = -7L + 13l lx + xL = -7L + 13l Add '-1lx' to each side of the equation. lx + -1lx + xL = -7L + 13l + -1lx Combine like terms: lx + -1lx = 0 0 + xL = -7L + 13l + -1lx xL = -7L + 13l + -1lx Add '-1xL' to each side of the equation. xL + -1xL = -7L + 13l + -1lx + -1xL Combine like terms: xL + -1xL = 0 0 = -7L + 13l + -1lx + -1xL Simplifying 0 = -7L + 13l + -1lx + -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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