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Simplifying 8ln(x + 3) + -6lnx = 0 Reorder the terms: 8ln(3 + x) + -6lnx = 0 (3 * 8ln + x * 8ln) + -6lnx = 0 (24ln + 8lnx) + -6lnx = 0 Combine like terms: 8lnx + -6lnx = 2lnx 24ln + 2lnx = 0 Solving 24ln + 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(12 + x) = 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 '(12 + x)' equal to zero and attempt to solve: Simplifying 12 + x = 0 Solving 12 + x = 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 + x = 0 + -12 Combine like terms: 12 + -12 = 0 0 + x = 0 + -12 x = 0 + -12 Combine like terms: 0 + -12 = -12 x = -12 Add '-1x' to each side of the equation. x + -1x = -12 + -1x Combine like terms: x + -1x = 0 0 = -12 + -1x Simplifying 0 = -12 + -1x 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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