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Simplifying 3lnx + 2ln(x + 1) = 0 Reorder the terms: 3lnx + 2ln(1 + x) = 0 3lnx + (1 * 2ln + x * 2ln) = 0 3lnx + (2ln + 2lnx) = 0 Reorder the terms: 2ln + 3lnx + 2lnx = 0 Combine like terms: 3lnx + 2lnx = 5lnx 2ln + 5lnx = 0 Solving 2ln + 5lnx = 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(2 + 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 '(2 + 5x)' equal to zero and attempt to solve: Simplifying 2 + 5x = 0 Solving 2 + 5x = 0 Move all terms containing l to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 5x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 5x = 0 + -2 5x = 0 + -2 Combine like terms: 0 + -2 = -2 5x = -2 Add '-5x' to each side of the equation. 5x + -5x = -2 + -5x Combine like terms: 5x + -5x = 0 0 = -2 + -5x Simplifying 0 = -2 + -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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