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Simplifying 3ln(x + 3) = ln(x + 3) * ln(x + 5) Reorder the terms: 3ln(3 + x) = ln(x + 3) * ln(x + 5) (3 * 3ln + x * 3ln) = ln(x + 3) * ln(x + 5) (9ln + 3lnx) = ln(x + 3) * ln(x + 5) Reorder the terms: 9ln + 3lnx = ln(3 + x) * ln(x + 5) Reorder the terms: 9ln + 3lnx = ln(3 + x) * ln(5 + x) Reorder the terms for easier multiplication: 9ln + 3lnx = ln * ln(3 + x)(5 + x) Multiply ln * ln 9ln + 3lnx = l2n2(3 + x)(5 + x) Multiply (3 + x) * (5 + x) 9ln + 3lnx = l2n2(3(5 + x) + x(5 + x)) 9ln + 3lnx = l2n2((5 * 3 + x * 3) + x(5 + x)) 9ln + 3lnx = l2n2((15 + 3x) + x(5 + x)) 9ln + 3lnx = l2n2(15 + 3x + (5 * x + x * x)) 9ln + 3lnx = l2n2(15 + 3x + (5x + x2)) Combine like terms: 3x + 5x = 8x 9ln + 3lnx = l2n2(15 + 8x + x2) 9ln + 3lnx = (15 * l2n2 + 8x * l2n2 + x2 * l2n2) 9ln + 3lnx = (15l2n2 + 8l2n2x + l2n2x2) Solving 9ln + 3lnx = 15l2n2 + 8l2n2x + l2n2x2 Solving for variable 'l'. Reorder the terms: 9ln + 3lnx + -15l2n2 + -8l2n2x + -1l2n2x2 = 15l2n2 + -15l2n2 + 8l2n2x + -8l2n2x + l2n2x2 + -1l2n2x2 Combine like terms: 15l2n2 + -15l2n2 = 0 9ln + 3lnx + -15l2n2 + -8l2n2x + -1l2n2x2 = 0 + 8l2n2x + -8l2n2x + l2n2x2 + -1l2n2x2 9ln + 3lnx + -15l2n2 + -8l2n2x + -1l2n2x2 = 8l2n2x + -8l2n2x + l2n2x2 + -1l2n2x2 Combine like terms: 8l2n2x + -8l2n2x = 0 9ln + 3lnx + -15l2n2 + -8l2n2x + -1l2n2x2 = 0 + l2n2x2 + -1l2n2x2 9ln + 3lnx + -15l2n2 + -8l2n2x + -1l2n2x2 = l2n2x2 + -1l2n2x2 Combine like terms: l2n2x2 + -1l2n2x2 = 0 9ln + 3lnx + -15l2n2 + -8l2n2x + -1l2n2x2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(9 + 3x + -15ln + -8lnx + -1lnx2) = 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 '(9 + 3x + -15ln + -8lnx + -1lnx2)' equal to zero and attempt to solve: Simplifying 9 + 3x + -15ln + -8lnx + -1lnx2 = 0 Reorder the terms: 9 + -15ln + -8lnx + -1lnx2 + 3x = 0 Solving 9 + -15ln + -8lnx + -1lnx2 + 3x = 0 Move all terms containing l to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -15ln + -8lnx + -1lnx2 + -9 + 3x = 0 + -9 Reorder the terms: 9 + -9 + -15ln + -8lnx + -1lnx2 + 3x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -15ln + -8lnx + -1lnx2 + 3x = 0 + -9 -15ln + -8lnx + -1lnx2 + 3x = 0 + -9 Combine like terms: 0 + -9 = -9 -15ln + -8lnx + -1lnx2 + 3x = -9 Add '-3x' to each side of the equation. -15ln + -8lnx + -1lnx2 + 3x + -3x = -9 + -3x Combine like terms: 3x + -3x = 0 -15ln + -8lnx + -1lnx2 + 0 = -9 + -3x -15ln + -8lnx + -1lnx2 = -9 + -3x 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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