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Simplifying 5ln(x + 5) + -2lnx = 0 Reorder the terms: 5ln(5 + x) + -2lnx = 0 (5 * 5ln + x * 5ln) + -2lnx = 0 (25ln + 5lnx) + -2lnx = 0 Combine like terms: 5lnx + -2lnx = 3lnx 25ln + 3lnx = 0 Solving 25ln + 3lnx = 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(25 + 3x) = 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 '(25 + 3x)' equal to zero and attempt to solve: Simplifying 25 + 3x = 0 Solving 25 + 3x = 0 Move all terms containing l to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + 3x = 0 + -25 Combine like terms: 25 + -25 = 0 0 + 3x = 0 + -25 3x = 0 + -25 Combine like terms: 0 + -25 = -25 3x = -25 Add '-3x' to each side of the equation. 3x + -3x = -25 + -3x Combine like terms: 3x + -3x = 0 0 = -25 + -3x Simplifying 0 = -25 + -3x 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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