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Simplifying 0 = 3ln(2x + 3) Reorder the terms: 0 = 3ln(3 + 2x) 0 = (3 * 3ln + 2x * 3ln) 0 = (9ln + 6lnx) Solving 0 = 9ln + 6lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-9ln' to each side of the equation. 0 + -9ln = 9ln + -9ln + 6lnx Remove the zero: -9ln = 9ln + -9ln + 6lnx Combine like terms: 9ln + -9ln = 0 -9ln = 0 + 6lnx -9ln = 6lnx Add '-6lnx' to each side of the equation. -9ln + -6lnx = 6lnx + -6lnx Combine like terms: 6lnx + -6lnx = 0 -9ln + -6lnx = 0 Factor out the Greatest Common Factor (GCF), '-3ln'. -3ln(3 + 2x) = 0 Ignore the factor -3.Subproblem 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 '(3 + 2x)' equal to zero and attempt to solve: Simplifying 3 + 2x = 0 Solving 3 + 2x = 0 Move all terms containing l to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2x = 0 + -3 2x = 0 + -3 Combine like terms: 0 + -3 = -3 2x = -3 Add '-2x' to each side of the equation. 2x + -2x = -3 + -2x Combine like terms: 2x + -2x = 0 0 = -3 + -2x Simplifying 0 = -3 + -2x 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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