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