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Simplifying 9ln(x + 6) + -4lnx = 0 Reorder the terms: 9ln(6 + x) + -4lnx = 0 (6 * 9ln + x * 9ln) + -4lnx = 0 (54ln + 9lnx) + -4lnx = 0 Combine like terms: 9lnx + -4lnx = 5lnx 54ln + 5lnx = 0 Solving 54ln + 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(54 + 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 '(54 + 5x)' equal to zero and attempt to solve: Simplifying 54 + 5x = 0 Solving 54 + 5x = 0 Move all terms containing l to the left, all other terms to the right. Add '-54' to each side of the equation. 54 + -54 + 5x = 0 + -54 Combine like terms: 54 + -54 = 0 0 + 5x = 0 + -54 5x = 0 + -54 Combine like terms: 0 + -54 = -54 5x = -54 Add '-5x' to each side of the equation. 5x + -5x = -54 + -5x Combine like terms: 5x + -5x = 0 0 = -54 + -5x Simplifying 0 = -54 + -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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