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Simplifying 6ln(x + 8) + -4lnx = 0 Reorder the terms: 6ln(8 + x) + -4lnx = 0 (8 * 6ln + x * 6ln) + -4lnx = 0 (48ln + 6lnx) + -4lnx = 0 Combine like terms: 6lnx + -4lnx = 2lnx 48ln + 2lnx = 0 Solving 48ln + 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(24 + 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 '(24 + x)' equal to zero and attempt to solve: Simplifying 24 + x = 0 Solving 24 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-24' to each side of the equation. 24 + -24 + x = 0 + -24 Combine like terms: 24 + -24 = 0 0 + x = 0 + -24 x = 0 + -24 Combine like terms: 0 + -24 = -24 x = -24 Add '-1x' to each side of the equation. x + -1x = -24 + -1x Combine like terms: x + -1x = 0 0 = -24 + -1x Simplifying 0 = -24 + -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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