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Simplifying 6ln(x + 9) + -8lnx = 0 Reorder the terms: 6ln(9 + x) + -8lnx = 0 (9 * 6ln + x * 6ln) + -8lnx = 0 (54ln + 6lnx) + -8lnx = 0 Combine like terms: 6lnx + -8lnx = -2lnx 54ln + -2lnx = 0 Solving 54ln + -2lnx = 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), '2ln'. 2ln(27 + -1x) = 0 Ignore the factor 2.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 + -1x)' equal to zero and attempt to solve: Simplifying 27 + -1x = 0 Solving 27 + -1x = 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 + -1x = 0 + -27 Combine like terms: 27 + -27 = 0 0 + -1x = 0 + -27 -1x = 0 + -27 Combine like terms: 0 + -27 = -27 -1x = -27 Add 'x' to each side of the equation. -1x + x = -27 + x Combine like terms: -1x + x = 0 0 = -27 + x Simplifying 0 = -27 + x 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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