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Simplifying 5ln(x) = ln(27) + -1ln(3) Multiply ln * x 5lnx = ln(27) + -1ln(3) Reorder the terms for easier multiplication: 5lnx = 27ln + -1ln(3) Reorder the terms for easier multiplication: 5lnx = 27ln + -1 * 3ln Multiply -1 * 3 5lnx = 27ln + -3ln Combine like terms: 27ln + -3ln = 24ln 5lnx = 24ln Solving 5lnx = 24ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-24ln' to each side of the equation. -24ln + 5lnx = 24ln + -24ln Combine like terms: 24ln + -24ln = 0 -24ln + 5lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-24 + 5x) = 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 + 5x)' equal to zero and attempt to solve: Simplifying -24 + 5x = 0 Solving -24 + 5x = 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 + 5x = 0 + 24 Combine like terms: -24 + 24 = 0 0 + 5x = 0 + 24 5x = 0 + 24 Combine like terms: 0 + 24 = 24 5x = 24 Add '-5x' to each side of the equation. 5x + -5x = 24 + -5x Combine like terms: 5x + -5x = 0 0 = 24 + -5x Simplifying 0 = 24 + -5x 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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