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Simplifying ln(x2) + 3lnx + -2ln(3x) = lny Multiply ln * x2 lnx2 + 3lnx + -2ln(3x) = lny Remove parenthesis around (3x) lnx2 + 3lnx + -2ln * 3x = lny Reorder the terms for easier multiplication: lnx2 + 3lnx + -2 * 3ln * x = lny Multiply -2 * 3 lnx2 + 3lnx + -6ln * x = lny Multiply ln * x lnx2 + 3lnx + -6lnx = lny Reorder the terms: 3lnx + -6lnx + lnx2 = lny Combine like terms: 3lnx + -6lnx = -3lnx -3lnx + lnx2 = lny Solving -3lnx + lnx2 = lny Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-1lny' to each side of the equation. -3lnx + lnx2 + -1lny = lny + -1lny Combine like terms: lny + -1lny = 0 -3lnx + lnx2 + -1lny = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-3x + x2 + -1y) = 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 '(-3x + x2 + -1y)' equal to zero and attempt to solve: Simplifying -3x + x2 + -1y = 0 Solving -3x + x2 + -1y = 0 Move all terms containing l to the left, all other terms to the right. Add '3x' to each side of the equation. -3x + x2 + 3x + -1y = 0 + 3x Reorder the terms: -3x + 3x + x2 + -1y = 0 + 3x Combine like terms: -3x + 3x = 0 0 + x2 + -1y = 0 + 3x x2 + -1y = 0 + 3x Remove the zero: x2 + -1y = 3x Add '-1x2' to each side of the equation. x2 + -1x2 + -1y = 3x + -1x2 Combine like terms: x2 + -1x2 = 0 0 + -1y = 3x + -1x2 -1y = 3x + -1x2 Add 'y' to each side of the equation. -1y + y = 3x + -1x2 + y Combine like terms: -1y + y = 0 0 = 3x + -1x2 + y Simplifying 0 = 3x + -1x2 + y 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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