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Simplifying Iny = lnx + ln(x + 20) + lnc Reorder the terms: nyI = lnx + ln(20 + x) + lnc nyI = lnx + (20 * ln + x * ln) + lnc nyI = lnx + (20ln + lnx) + lnc Reorder the terms: nyI = cln + 20ln + lnx + lnx Combine like terms: lnx + lnx = 2lnx nyI = cln + 20ln + 2lnx Solving nyI = cln + 20ln + 2lnx Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-1cln' to each side of the equation. -1cln + nyI = cln + 20ln + -1cln + 2lnx Reorder the terms: -1cln + nyI = cln + -1cln + 20ln + 2lnx Combine like terms: cln + -1cln = 0 -1cln + nyI = 0 + 20ln + 2lnx -1cln + nyI = 20ln + 2lnx Add '-20ln' to each side of the equation. -1cln + -20ln + nyI = 20ln + -20ln + 2lnx Combine like terms: 20ln + -20ln = 0 -1cln + -20ln + nyI = 0 + 2lnx -1cln + -20ln + nyI = 2lnx Add '-2lnx' to each side of the equation. -1cln + -20ln + -2lnx + nyI = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 -1cln + -20ln + -2lnx + nyI = 0 Factor out the Greatest Common Factor (GCF), 'n'. n(-1cl + -20l + -2lx + yI) = 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 '(-1cl + -20l + -2lx + yI)' equal to zero and attempt to solve: Simplifying -1cl + -20l + -2lx + yI = 0 Solving -1cl + -20l + -2lx + yI = 0 Move all terms containing n to the left, all other terms to the right. Add 'cl' to each side of the equation. -1cl + -20l + -2lx + cl + yI = 0 + cl Reorder the terms: -1cl + cl + -20l + -2lx + yI = 0 + cl Combine like terms: -1cl + cl = 0 0 + -20l + -2lx + yI = 0 + cl -20l + -2lx + yI = 0 + cl Remove the zero: -20l + -2lx + yI = cl Add '20l' to each side of the equation. -20l + -2lx + 20l + yI = cl + 20l Reorder the terms: -20l + 20l + -2lx + yI = cl + 20l Combine like terms: -20l + 20l = 0 0 + -2lx + yI = cl + 20l -2lx + yI = cl + 20l Add '2lx' to each side of the equation. -2lx + 2lx + yI = cl + 20l + 2lx Combine like terms: -2lx + 2lx = 0 0 + yI = cl + 20l + 2lx yI = cl + 20l + 2lx Add '-1yI' to each side of the equation. yI + -1yI = cl + 20l + 2lx + -1yI Combine like terms: yI + -1yI = 0 0 = cl + 20l + 2lx + -1yI Simplifying 0 = cl + 20l + 2lx + -1yI 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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