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Simplifying 2ln(x + -3) + -1ln(x + -9) = 2ln(5) Reorder the terms: 2ln(-3 + x) + -1ln(x + -9) = 2ln(5) (-3 * 2ln + x * 2ln) + -1ln(x + -9) = 2ln(5) (-6ln + 2lnx) + -1ln(x + -9) = 2ln(5) Reorder the terms: -6ln + 2lnx + -1ln(-9 + x) = 2ln(5) -6ln + 2lnx + (-9 * -1ln + x * -1ln) = 2ln(5) -6ln + 2lnx + (9ln + -1lnx) = 2ln(5) Reorder the terms: -6ln + 9ln + 2lnx + -1lnx = 2ln(5) Combine like terms: -6ln + 9ln = 3ln 3ln + 2lnx + -1lnx = 2ln(5) Combine like terms: 2lnx + -1lnx = 1lnx 3ln + 1lnx = 2ln(5) Reorder the terms for easier multiplication: 3ln + 1lnx = 2 * 5ln Multiply 2 * 5 3ln + 1lnx = 10ln Solving 3ln + 1lnx = 10ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-10ln' to each side of the equation. 3ln + -10ln + 1lnx = 10ln + -10ln Combine like terms: 3ln + -10ln = -7ln -7ln + 1lnx = 10ln + -10ln Combine like terms: 10ln + -10ln = 0 -7ln + 1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-7 + x) = 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 '(-7 + x)' equal to zero and attempt to solve: Simplifying -7 + x = 0 Solving -7 + x = 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 + x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + x = 0 + 7 x = 0 + 7 Combine like terms: 0 + 7 = 7 x = 7 Add '-1x' to each side of the equation. x + -1x = 7 + -1x Combine like terms: x + -1x = 0 0 = 7 + -1x Simplifying 0 = 7 + -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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