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Simplifying lny = lnx + ln(sqrt(2x2 + 5x + 2)) Reorder the terms: lny = lnx + ln(qrst(2 + 5x + 2x2)) lny = lnx + ln((2 * qrst + 5x * qrst + 2x2 * qrst)) lny = lnx + ln((2qrst + 5qrstx + 2qrstx2)) lny = lnx + (2qrst * ln + 5qrstx * ln + 2qrstx2 * ln) lny = lnx + (2lnqrst + 5lnqrstx + 2lnqrstx2) Reorder the terms: lny = 2lnqrst + 5lnqrstx + 2lnqrstx2 + lnx Solving lny = 2lnqrst + 5lnqrstx + 2lnqrstx2 + lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-2lnqrst' to each side of the equation. -2lnqrst + lny = 2lnqrst + 5lnqrstx + 2lnqrstx2 + -2lnqrst + lnx Reorder the terms: -2lnqrst + lny = 2lnqrst + -2lnqrst + 5lnqrstx + 2lnqrstx2 + lnx Combine like terms: 2lnqrst + -2lnqrst = 0 -2lnqrst + lny = 0 + 5lnqrstx + 2lnqrstx2 + lnx -2lnqrst + lny = 5lnqrstx + 2lnqrstx2 + lnx Add '-5lnqrstx' to each side of the equation. -2lnqrst + -5lnqrstx + lny = 5lnqrstx + 2lnqrstx2 + -5lnqrstx + lnx Reorder the terms: -2lnqrst + -5lnqrstx + lny = 5lnqrstx + -5lnqrstx + 2lnqrstx2 + lnx Combine like terms: 5lnqrstx + -5lnqrstx = 0 -2lnqrst + -5lnqrstx + lny = 0 + 2lnqrstx2 + lnx -2lnqrst + -5lnqrstx + lny = 2lnqrstx2 + lnx Add '-2lnqrstx2' to each side of the equation. -2lnqrst + -5lnqrstx + -2lnqrstx2 + lny = 2lnqrstx2 + -2lnqrstx2 + lnx Combine like terms: 2lnqrstx2 + -2lnqrstx2 = 0 -2lnqrst + -5lnqrstx + -2lnqrstx2 + lny = 0 + lnx -2lnqrst + -5lnqrstx + -2lnqrstx2 + lny = lnx Add '-1lnx' to each side of the equation. -2lnqrst + -5lnqrstx + -2lnqrstx2 + -1lnx + lny = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -2lnqrst + -5lnqrstx + -2lnqrstx2 + -1lnx + lny = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-2qrst + -5qrstx + -2qrstx2 + -1x + y) = 0Subproblem 1
Set the factor 'ln' equal to zero and attempt to solve: Simplifying ln = 0 Solving ln = 0 Move all terms containing l to the left, all other terms to the right. Simplifying ln = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(-2qrst + -5qrstx + -2qrstx2 + -1x + y)' equal to zero and attempt to solve: Simplifying -2qrst + -5qrstx + -2qrstx2 + -1x + y = 0 Solving -2qrst + -5qrstx + -2qrstx2 + -1x + y = 0 Move all terms containing l to the left, all other terms to the right. Add '2qrst' to each side of the equation. -2qrst + -5qrstx + -2qrstx2 + -1x + 2qrst + y = 0 + 2qrst Reorder the terms: -2qrst + 2qrst + -5qrstx + -2qrstx2 + -1x + y = 0 + 2qrst Combine like terms: -2qrst + 2qrst = 0 0 + -5qrstx + -2qrstx2 + -1x + y = 0 + 2qrst -5qrstx + -2qrstx2 + -1x + y = 0 + 2qrst Remove the zero: -5qrstx + -2qrstx2 + -1x + y = 2qrst Add '5qrstx' to each side of the equation. -5qrstx + -2qrstx2 + -1x + 5qrstx + y = 2qrst + 5qrstx Reorder the terms: -5qrstx + 5qrstx + -2qrstx2 + -1x + y = 2qrst + 5qrstx Combine like terms: -5qrstx + 5qrstx = 0 0 + -2qrstx2 + -1x + y = 2qrst + 5qrstx -2qrstx2 + -1x + y = 2qrst + 5qrstx Add '2qrstx2' to each side of the equation. -2qrstx2 + -1x + 2qrstx2 + y = 2qrst + 5qrstx + 2qrstx2 Reorder the terms: -2qrstx2 + 2qrstx2 + -1x + y = 2qrst + 5qrstx + 2qrstx2 Combine like terms: -2qrstx2 + 2qrstx2 = 0 0 + -1x + y = 2qrst + 5qrstx + 2qrstx2 -1x + y = 2qrst + 5qrstx + 2qrstx2 Add 'x' to each side of the equation. -1x + x + y = 2qrst + 5qrstx + 2qrstx2 + x Combine like terms: -1x + x = 0 0 + y = 2qrst + 5qrstx + 2qrstx2 + x y = 2qrst + 5qrstx + 2qrstx2 + x Add '-1y' to each side of the equation. y + -1y = 2qrst + 5qrstx + 2qrstx2 + x + -1y Combine like terms: y + -1y = 0 0 = 2qrst + 5qrstx + 2qrstx2 + x + -1y Simplifying 0 = 2qrst + 5qrstx + 2qrstx2 + x + -1y The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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