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Simplifying 5ln(x + 2) + -8lnx = 0 Reorder the terms: 5ln(2 + x) + -8lnx = 0 (2 * 5ln + x * 5ln) + -8lnx = 0 (10ln + 5lnx) + -8lnx = 0 Combine like terms: 5lnx + -8lnx = -3lnx 10ln + -3lnx = 0 Solving 10ln + -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(10 + -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 '(10 + -3x)' equal to zero and attempt to solve: Simplifying 10 + -3x = 0 Solving 10 + -3x = 0 Move all terms containing l to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -3x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -3x = 0 + -10 -3x = 0 + -10 Combine like terms: 0 + -10 = -10 -3x = -10 Add '3x' to each side of the equation. -3x + 3x = -10 + 3x Combine like terms: -3x + 3x = 0 0 = -10 + 3x Simplifying 0 = -10 + 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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