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Simplifying ln((2x + 9)(x + 9)) = 2ln(x + 9) Reorder the terms: ln((9 + 2x)(x + 9)) = 2ln(x + 9) Reorder the terms: ln((9 + 2x)(9 + x)) = 2ln(x + 9) Multiply (9 + 2x) * (9 + x) ln((9(9 + x) + 2x * (9 + x))) = 2ln(x + 9) ln(((9 * 9 + x * 9) + 2x * (9 + x))) = 2ln(x + 9) ln(((81 + 9x) + 2x * (9 + x))) = 2ln(x + 9) ln((81 + 9x + (9 * 2x + x * 2x))) = 2ln(x + 9) ln((81 + 9x + (18x + 2x2))) = 2ln(x + 9) Combine like terms: 9x + 18x = 27x ln((81 + 27x + 2x2)) = 2ln(x + 9) (81 * ln + 27x * ln + 2x2 * ln) = 2ln(x + 9) (81ln + 27lnx + 2lnx2) = 2ln(x + 9) Reorder the terms: 81ln + 27lnx + 2lnx2 = 2ln(9 + x) 81ln + 27lnx + 2lnx2 = (9 * 2ln + x * 2ln) 81ln + 27lnx + 2lnx2 = (18ln + 2lnx) Solving 81ln + 27lnx + 2lnx2 = 18ln + 2lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-18ln' to each side of the equation. 81ln + 27lnx + -18ln + 2lnx2 = 18ln + -18ln + 2lnx Reorder the terms: 81ln + -18ln + 27lnx + 2lnx2 = 18ln + -18ln + 2lnx Combine like terms: 81ln + -18ln = 63ln 63ln + 27lnx + 2lnx2 = 18ln + -18ln + 2lnx Combine like terms: 18ln + -18ln = 0 63ln + 27lnx + 2lnx2 = 0 + 2lnx 63ln + 27lnx + 2lnx2 = 2lnx Add '-2lnx' to each side of the equation. 63ln + 27lnx + -2lnx + 2lnx2 = 2lnx + -2lnx Combine like terms: 27lnx + -2lnx = 25lnx 63ln + 25lnx + 2lnx2 = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 63ln + 25lnx + 2lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(63 + 25x + 2x2) = 0 Factor a trinomial. ln((9 + x)(7 + 2x)) = 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 + x)' equal to zero and attempt to solve: Simplifying 9 + x = 0 Solving 9 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + x = 0 + -9 x = 0 + -9 Combine like terms: 0 + -9 = -9 x = -9 Add '-1x' to each side of the equation. x + -1x = -9 + -1x Combine like terms: x + -1x = 0 0 = -9 + -1x Simplifying 0 = -9 + -1x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(7 + 2x)' equal to zero and attempt to solve: Simplifying 7 + 2x = 0 Solving 7 + 2x = 0 Move all terms containing l to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 2x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 2x = 0 + -7 2x = 0 + -7 Combine like terms: 0 + -7 = -7 2x = -7 Add '-2x' to each side of the equation. 2x + -2x = -7 + -2x Combine like terms: 2x + -2x = 0 0 = -7 + -2x Simplifying 0 = -7 + -2x 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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