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Simplifying 9ln(x) + -8ln(3x) = 2ln(6) Multiply ln * x 9lnx + -8ln(3x) = 2ln(6) Remove parenthesis around (3x) 9lnx + -8ln * 3x = 2ln(6) Reorder the terms for easier multiplication: 9lnx + -8 * 3ln * x = 2ln(6) Multiply -8 * 3 9lnx + -24ln * x = 2ln(6) Multiply ln * x 9lnx + -24lnx = 2ln(6) Combine like terms: 9lnx + -24lnx = -15lnx -15lnx = 2ln(6) Reorder the terms for easier multiplication: -15lnx = 2 * 6ln Multiply 2 * 6 -15lnx = 12ln Solving -15lnx = 12ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-12ln' to each side of the equation. -12ln + -15lnx = 12ln + -12ln Combine like terms: 12ln + -12ln = 0 -12ln + -15lnx = 0 Factor out the Greatest Common Factor (GCF), '-3ln'. -3ln(4 + 5x) = 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 '(4 + 5x)' equal to zero and attempt to solve: Simplifying 4 + 5x = 0 Solving 4 + 5x = 0 Move all terms containing l to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + 5x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 5x = 0 + -4 5x = 0 + -4 Combine like terms: 0 + -4 = -4 5x = -4 Add '-5x' to each side of the equation. 5x + -5x = -4 + -5x Combine like terms: 5x + -5x = 0 0 = -4 + -5x Simplifying 0 = -4 + -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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