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Simplifying ln(x + -9) + -2ln(x + -3) = -2ln(5) Reorder the terms: ln(-9 + x) + -2ln(x + -3) = -2ln(5) (-9 * ln + x * ln) + -2ln(x + -3) = -2ln(5) (-9ln + lnx) + -2ln(x + -3) = -2ln(5) Reorder the terms: -9ln + lnx + -2ln(-3 + x) = -2ln(5) -9ln + lnx + (-3 * -2ln + x * -2ln) = -2ln(5) -9ln + lnx + (6ln + -2lnx) = -2ln(5) Reorder the terms: -9ln + 6ln + lnx + -2lnx = -2ln(5) Combine like terms: -9ln + 6ln = -3ln -3ln + lnx + -2lnx = -2ln(5) Combine like terms: lnx + -2lnx = -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 + -1x) = 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 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 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 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Add 'x' to each side of the equation. -1x + x = -7 + x Combine like terms: -1x + x = 0 0 = -7 + x Simplifying 0 = -7 + x 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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