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Simplifying 8ln(x) + -9ln(3x) = 2ln(6) Multiply ln * x 8lnx + -9ln(3x) = 2ln(6) Remove parenthesis around (3x) 8lnx + -9ln * 3x = 2ln(6) Reorder the terms for easier multiplication: 8lnx + -9 * 3ln * x = 2ln(6) Multiply -9 * 3 8lnx + -27ln * x = 2ln(6) Multiply ln * x 8lnx + -27lnx = 2ln(6) Combine like terms: 8lnx + -27lnx = -19lnx -19lnx = 2ln(6) Reorder the terms for easier multiplication: -19lnx = 2 * 6ln Multiply 2 * 6 -19lnx = 12ln Solving -19lnx = 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 + -19lnx = 12ln + -12ln Combine like terms: 12ln + -12ln = 0 -12ln + -19lnx = 0 Factor out the Greatest Common Factor (GCF), '-1ln'. -1ln(12 + 19x) = 0 Ignore the factor -1.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 '(12 + 19x)' equal to zero and attempt to solve: Simplifying 12 + 19x = 0 Solving 12 + 19x = 0 Move all terms containing l to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + 19x = 0 + -12 Combine like terms: 12 + -12 = 0 0 + 19x = 0 + -12 19x = 0 + -12 Combine like terms: 0 + -12 = -12 19x = -12 Add '-19x' to each side of the equation. 19x + -19x = -12 + -19x Combine like terms: 19x + -19x = 0 0 = -12 + -19x Simplifying 0 = -12 + -19x 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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