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Simplifying ln(x + -9) + -2ln(x + 3) = -2ln(7) Reorder the terms: ln(-9 + x) + -2ln(x + 3) = -2ln(7) (-9 * ln + x * ln) + -2ln(x + 3) = -2ln(7) (-9ln + lnx) + -2ln(x + 3) = -2ln(7) Reorder the terms: -9ln + lnx + -2ln(3 + x) = -2ln(7) -9ln + lnx + (3 * -2ln + x * -2ln) = -2ln(7) -9ln + lnx + (-6ln + -2lnx) = -2ln(7) Reorder the terms: -9ln + -6ln + lnx + -2lnx = -2ln(7) Combine like terms: -9ln + -6ln = -15ln -15ln + lnx + -2lnx = -2ln(7) Combine like terms: lnx + -2lnx = -1lnx -15ln + -1lnx = -2ln(7) Reorder the terms for easier multiplication: -15ln + -1lnx = -2 * 7ln Multiply -2 * 7 -15ln + -1lnx = -14ln Solving -15ln + -1lnx = -14ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '14ln' to each side of the equation. -15ln + 14ln + -1lnx = -14ln + 14ln Combine like terms: -15ln + 14ln = -1ln -1ln + -1lnx = -14ln + 14ln Combine like terms: -14ln + 14ln = 0 -1ln + -1lnx = 0 Factor out the Greatest Common Factor (GCF), '-1ln'. -1ln(1 + x) = 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 '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Add '-1x' to each side of the equation. x + -1x = -1 + -1x Combine like terms: x + -1x = 0 0 = -1 + -1x Simplifying 0 = -1 + -1x 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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