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Simplifying 4ln(x + 6) + -5lnx = 0 Reorder the terms: 4ln(6 + x) + -5lnx = 0 (6 * 4ln + x * 4ln) + -5lnx = 0 (24ln + 4lnx) + -5lnx = 0 Combine like terms: 4lnx + -5lnx = -1lnx 24ln + -1lnx = 0 Solving 24ln + -1lnx = 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), 'ln'. ln(24 + -1x) = 0Subproblem 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 + -1x)' equal to zero and attempt to solve: Simplifying 24 + -1x = 0 Solving 24 + -1x = 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 + -1x = 0 + -24 Combine like terms: 24 + -24 = 0 0 + -1x = 0 + -24 -1x = 0 + -24 Combine like terms: 0 + -24 = -24 -1x = -24 Add 'x' to each side of the equation. -1x + x = -24 + x Combine like terms: -1x + x = 0 0 = -24 + x Simplifying 0 = -24 + 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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