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Simplifying ln(2x + 5) + ln(x + -9) + -2ln(x) = 0 Reorder the terms: ln(5 + 2x) + ln(x + -9) + -2ln(x) = 0 (5 * ln + 2x * ln) + ln(x + -9) + -2ln(x) = 0 (5ln + 2lnx) + ln(x + -9) + -2ln(x) = 0 Reorder the terms: 5ln + 2lnx + ln(-9 + x) + -2ln(x) = 0 5ln + 2lnx + (-9 * ln + x * ln) + -2ln(x) = 0 5ln + 2lnx + (-9ln + lnx) + -2ln(x) = 0 Multiply ln * x 5ln + 2lnx + -9ln + lnx + -2lnx = 0 Reorder the terms: 5ln + -9ln + 2lnx + lnx + -2lnx = 0 Combine like terms: 5ln + -9ln = -4ln -4ln + 2lnx + lnx + -2lnx = 0 Combine like terms: 2lnx + lnx = 3lnx -4ln + 3lnx + -2lnx = 0 Combine like terms: 3lnx + -2lnx = 1lnx -4ln + 1lnx = 0 Solving -4ln + 1lnx = 0 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), 'ln'. ln(-4 + 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 '(-4 + x)' equal to zero and attempt to solve: Simplifying -4 + x = 0 Solving -4 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + x = 0 + 4 x = 0 + 4 Combine like terms: 0 + 4 = 4 x = 4 Add '-1x' to each side of the equation. x + -1x = 4 + -1x Combine like terms: x + -1x = 0 0 = 4 + -1x Simplifying 0 = 4 + -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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