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Simplifying ln(6x2 + x + -15) + -1ln(3x + 5) = ln(5x + 15) Reorder the terms: ln(-15 + x + 6x2) + -1ln(3x + 5) = ln(5x + 15) (-15 * ln + x * ln + 6x2 * ln) + -1ln(3x + 5) = ln(5x + 15) (-15ln + lnx + 6lnx2) + -1ln(3x + 5) = ln(5x + 15) Reorder the terms: -15ln + lnx + 6lnx2 + -1ln(5 + 3x) = ln(5x + 15) -15ln + lnx + 6lnx2 + (5 * -1ln + 3x * -1ln) = ln(5x + 15) -15ln + lnx + 6lnx2 + (-5ln + -3lnx) = ln(5x + 15) Reorder the terms: -15ln + -5ln + lnx + -3lnx + 6lnx2 = ln(5x + 15) Combine like terms: -15ln + -5ln = -20ln -20ln + lnx + -3lnx + 6lnx2 = ln(5x + 15) Combine like terms: lnx + -3lnx = -2lnx -20ln + -2lnx + 6lnx2 = ln(5x + 15) Reorder the terms: -20ln + -2lnx + 6lnx2 = ln(15 + 5x) -20ln + -2lnx + 6lnx2 = (15 * ln + 5x * ln) -20ln + -2lnx + 6lnx2 = (15ln + 5lnx) Solving -20ln + -2lnx + 6lnx2 = 15ln + 5lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-15ln' to each side of the equation. -20ln + -2lnx + -15ln + 6lnx2 = 15ln + -15ln + 5lnx Reorder the terms: -20ln + -15ln + -2lnx + 6lnx2 = 15ln + -15ln + 5lnx Combine like terms: -20ln + -15ln = -35ln -35ln + -2lnx + 6lnx2 = 15ln + -15ln + 5lnx Combine like terms: 15ln + -15ln = 0 -35ln + -2lnx + 6lnx2 = 0 + 5lnx -35ln + -2lnx + 6lnx2 = 5lnx Add '-5lnx' to each side of the equation. -35ln + -2lnx + -5lnx + 6lnx2 = 5lnx + -5lnx Combine like terms: -2lnx + -5lnx = -7lnx -35ln + -7lnx + 6lnx2 = 5lnx + -5lnx Combine like terms: 5lnx + -5lnx = 0 -35ln + -7lnx + 6lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-35 + -7x + 6x2) = 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 '(-35 + -7x + 6x2)' equal to zero and attempt to solve: Simplifying -35 + -7x + 6x2 = 0 Solving -35 + -7x + 6x2 = 0 Move all terms containing l to the left, all other terms to the right. Add '35' to each side of the equation. -35 + -7x + 35 + 6x2 = 0 + 35 Reorder the terms: -35 + 35 + -7x + 6x2 = 0 + 35 Combine like terms: -35 + 35 = 0 0 + -7x + 6x2 = 0 + 35 -7x + 6x2 = 0 + 35 Combine like terms: 0 + 35 = 35 -7x + 6x2 = 35 Add '7x' to each side of the equation. -7x + 7x + 6x2 = 35 + 7x Combine like terms: -7x + 7x = 0 0 + 6x2 = 35 + 7x 6x2 = 35 + 7x Add '-6x2' to each side of the equation. 6x2 + -6x2 = 35 + 7x + -6x2 Combine like terms: 6x2 + -6x2 = 0 0 = 35 + 7x + -6x2 Simplifying 0 = 35 + 7x + -6x2 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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