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Simplifying ln(3 + -1x) + -2ln(x) = ln(4) (3 * ln + -1x * ln) + -2ln(x) = ln(4) (3ln + -1lnx) + -2ln(x) = ln(4) Multiply ln * x 3ln + -1lnx + -2lnx = ln(4) Combine like terms: -1lnx + -2lnx = -3lnx 3ln + -3lnx = ln(4) Reorder the terms for easier multiplication: 3ln + -3lnx = 4ln Solving 3ln + -3lnx = 4ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-4ln' to each side of the equation. 3ln + -4ln + -3lnx = 4ln + -4ln Combine like terms: 3ln + -4ln = -1ln -1ln + -3lnx = 4ln + -4ln Combine like terms: 4ln + -4ln = 0 -1ln + -3lnx = 0 Factor out the Greatest Common Factor (GCF), '-1ln'. -1ln(1 + 3x) = 0 Ignore the factor -1.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 + 3x)' equal to zero and attempt to solve: Simplifying 1 + 3x = 0 Solving 1 + 3x = 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 + 3x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3x = 0 + -1 3x = 0 + -1 Combine like terms: 0 + -1 = -1 3x = -1 Add '-3x' to each side of the equation. 3x + -3x = -1 + -3x Combine like terms: 3x + -3x = 0 0 = -1 + -3x Simplifying 0 = -1 + -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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