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Simplifying 9ln(x + 3) + -4ln(x) = 0 Reorder the terms: 9ln(3 + x) + -4ln(x) = 0 (3 * 9ln + x * 9ln) + -4ln(x) = 0 (27ln + 9lnx) + -4ln(x) = 0 Multiply ln * x 27ln + 9lnx + -4lnx = 0 Combine like terms: 9lnx + -4lnx = 5lnx 27ln + 5lnx = 0 Solving 27ln + 5lnx = 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(27 + 5x) = 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 '(27 + 5x)' equal to zero and attempt to solve: Simplifying 27 + 5x = 0 Solving 27 + 5x = 0 Move all terms containing l to the left, all other terms to the right. Add '-27' to each side of the equation. 27 + -27 + 5x = 0 + -27 Combine like terms: 27 + -27 = 0 0 + 5x = 0 + -27 5x = 0 + -27 Combine like terms: 0 + -27 = -27 5x = -27 Add '-5x' to each side of the equation. 5x + -5x = -27 + -5x Combine like terms: 5x + -5x = 0 0 = -27 + -5x Simplifying 0 = -27 + -5x 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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