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Simplifying 2lnx + 3ln(1 + x) + -4ln(2x) = 0 2lnx + (1 * 3ln + x * 3ln) + -4ln(2x) = 0 2lnx + (3ln + 3lnx) + -4ln(2x) = 0 Remove parenthesis around (2x) 2lnx + 3ln + 3lnx + -4ln * 2x = 0 Reorder the terms for easier multiplication: 2lnx + 3ln + 3lnx + -4 * 2ln * x = 0 Multiply -4 * 2 2lnx + 3ln + 3lnx + -8ln * x = 0 Multiply ln * x 2lnx + 3ln + 3lnx + -8lnx = 0 Reorder the terms: 3ln + 2lnx + 3lnx + -8lnx = 0 Combine like terms: 2lnx + 3lnx = 5lnx 3ln + 5lnx + -8lnx = 0 Combine like terms: 5lnx + -8lnx = -3lnx 3ln + -3lnx = 0 Solving 3ln + -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), '3ln'. 3ln(1 + -1x) = 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 '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Add 'x' to each side of the equation. -1x + x = -1 + x Combine like terms: -1x + x = 0 0 = -1 + x Simplifying 0 = -1 + x 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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