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Simplifying Ln(9r + 1) = ln(r + 9) Reorder the terms: nL(1 + 9r) = ln(r + 9) (1 * nL + 9r * nL) = ln(r + 9) (1nL + 9nrL) = ln(r + 9) Reorder the terms: 1nL + 9nrL = ln(9 + r) 1nL + 9nrL = (9 * ln + r * ln) 1nL + 9nrL = (9ln + lnr) Solving 1nL + 9nrL = 9ln + lnr Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-9ln' to each side of the equation. 1nL + -9ln + 9nrL = 9ln + -9ln + lnr Reorder the terms: -9ln + 1nL + 9nrL = 9ln + -9ln + lnr Combine like terms: 9ln + -9ln = 0 -9ln + 1nL + 9nrL = 0 + lnr -9ln + 1nL + 9nrL = lnr Add '-1lnr' to each side of the equation. -9ln + 1nL + -1lnr + 9nrL = lnr + -1lnr Reorder the terms: -9ln + -1lnr + 1nL + 9nrL = lnr + -1lnr Combine like terms: lnr + -1lnr = 0 -9ln + -1lnr + 1nL + 9nrL = 0 Factor out the Greatest Common Factor (GCF), 'n'. n(-9l + -1lr + L + 9rL) = 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 '(-9l + -1lr + L + 9rL)' equal to zero and attempt to solve: Simplifying -9l + -1lr + L + 9rL = 0 Reorder the terms: L + -9l + -1lr + 9rL = 0 Solving L + -9l + -1lr + 9rL = 0 Move all terms containing n to the left, all other terms to the right. Add '-1L' to each side of the equation. L + -9l + -1lr + -1L + 9rL = 0 + -1L Reorder the terms: L + -1L + -9l + -1lr + 9rL = 0 + -1L Combine like terms: L + -1L = 0 0 + -9l + -1lr + 9rL = 0 + -1L -9l + -1lr + 9rL = 0 + -1L Remove the zero: -9l + -1lr + 9rL = -1L Add '9l' to each side of the equation. -9l + -1lr + 9l + 9rL = -1L + 9l Reorder the terms: -9l + 9l + -1lr + 9rL = -1L + 9l Combine like terms: -9l + 9l = 0 0 + -1lr + 9rL = -1L + 9l -1lr + 9rL = -1L + 9l Add 'lr' to each side of the equation. -1lr + lr + 9rL = -1L + 9l + lr Combine like terms: -1lr + lr = 0 0 + 9rL = -1L + 9l + lr 9rL = -1L + 9l + lr Add '-9rL' to each side of the equation. 9rL + -9rL = -1L + 9l + lr + -9rL Combine like terms: 9rL + -9rL = 0 0 = -1L + 9l + lr + -9rL Simplifying 0 = -1L + 9l + lr + -9rL 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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