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