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Simplifying 3ln(x + 2) + -8lnx = 0 Reorder the terms: 3ln(2 + x) + -8lnx = 0 (2 * 3ln + x * 3ln) + -8lnx = 0 (6ln + 3lnx) + -8lnx = 0 Combine like terms: 3lnx + -8lnx = -5lnx 6ln + -5lnx = 0 Solving 6ln + -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(6 + -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 '(6 + -5x)' equal to zero and attempt to solve: Simplifying 6 + -5x = 0 Solving 6 + -5x = 0 Move all terms containing l to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -5x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -5x = 0 + -6 -5x = 0 + -6 Combine like terms: 0 + -6 = -6 -5x = -6 Add '5x' to each side of the equation. -5x + 5x = -6 + 5x Combine like terms: -5x + 5x = 0 0 = -6 + 5x Simplifying 0 = -6 + 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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