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Simplifying 9ln(x + 9) + -6ln(x) = 0 Reorder the terms: 9ln(9 + x) + -6ln(x) = 0 (9 * 9ln + x * 9ln) + -6ln(x) = 0 (81ln + 9lnx) + -6ln(x) = 0 Multiply ln * x 81ln + 9lnx + -6lnx = 0 Combine like terms: 9lnx + -6lnx = 3lnx 81ln + 3lnx = 0 Solving 81ln + 3lnx = 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), '3ln'. 3ln(27 + x) = 0 Ignore the factor 3.Subproblem 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 + x)' equal to zero and attempt to solve: Simplifying 27 + x = 0 Solving 27 + x = 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 + x = 0 + -27 Combine like terms: 27 + -27 = 0 0 + x = 0 + -27 x = 0 + -27 Combine like terms: 0 + -27 = -27 x = -27 Add '-1x' to each side of the equation. x + -1x = -27 + -1x Combine like terms: x + -1x = 0 0 = -27 + -1x Simplifying 0 = -27 + -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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