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Simplifying 3ln(x + 9) + -5lnx = 0 Reorder the terms: 3ln(9 + x) + -5lnx = 0 (9 * 3ln + x * 3ln) + -5lnx = 0 (27ln + 3lnx) + -5lnx = 0 Combine like terms: 3lnx + -5lnx = -2lnx 27ln + -2lnx = 0 Solving 27ln + -2lnx = 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 + -2x) = 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 + -2x)' equal to zero and attempt to solve: Simplifying 27 + -2x = 0 Solving 27 + -2x = 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 + -2x = 0 + -27 Combine like terms: 27 + -27 = 0 0 + -2x = 0 + -27 -2x = 0 + -27 Combine like terms: 0 + -27 = -27 -2x = -27 Add '2x' to each side of the equation. -2x + 2x = -27 + 2x Combine like terms: -2x + 2x = 0 0 = -27 + 2x Simplifying 0 = -27 + 2x 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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