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Simplifying -3ln(9) + -3ln(x) + -4ln(x2 + 9) = ln Reorder the terms for easier multiplication: -3 * 9ln + -3ln(x) + -4ln(x2 + 9) = ln Multiply -3 * 9 -27ln + -3ln(x) + -4ln(x2 + 9) = ln Multiply ln * x -27ln + -3lnx + -4ln(x2 + 9) = ln Reorder the terms: -27ln + -3lnx + -4ln(9 + x2) = ln -27ln + -3lnx + (9 * -4ln + x2 * -4ln) = ln -27ln + -3lnx + (-36ln + -4lnx2) = ln Reorder the terms: -27ln + -36ln + -3lnx + -4lnx2 = ln Combine like terms: -27ln + -36ln = -63ln -63ln + -3lnx + -4lnx2 = ln Solving -63ln + -3lnx + -4lnx2 = ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-1ln' to each side of the equation. -63ln + -3lnx + -1ln + -4lnx2 = ln + -1ln Reorder the terms: -63ln + -1ln + -3lnx + -4lnx2 = ln + -1ln Combine like terms: -63ln + -1ln = -64ln -64ln + -3lnx + -4lnx2 = ln + -1ln Combine like terms: ln + -1ln = 0 -64ln + -3lnx + -4lnx2 = 0 Factor out the Greatest Common Factor (GCF), '-1ln'. -1ln(64 + 3x + 4x2) = 0 Ignore the factor -1.Subproblem 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 '(64 + 3x + 4x2)' equal to zero and attempt to solve: Simplifying 64 + 3x + 4x2 = 0 Solving 64 + 3x + 4x2 = 0 Move all terms containing l to the left, all other terms to the right. Add '-64' to each side of the equation. 64 + 3x + -64 + 4x2 = 0 + -64 Reorder the terms: 64 + -64 + 3x + 4x2 = 0 + -64 Combine like terms: 64 + -64 = 0 0 + 3x + 4x2 = 0 + -64 3x + 4x2 = 0 + -64 Combine like terms: 0 + -64 = -64 3x + 4x2 = -64 Add '-3x' to each side of the equation. 3x + -3x + 4x2 = -64 + -3x Combine like terms: 3x + -3x = 0 0 + 4x2 = -64 + -3x 4x2 = -64 + -3x Add '-4x2' to each side of the equation. 4x2 + -4x2 = -64 + -3x + -4x2 Combine like terms: 4x2 + -4x2 = 0 0 = -64 + -3x + -4x2 Simplifying 0 = -64 + -3x + -4x2 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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