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Simplifying 2ln(3x + 1) + -1ln(x + 1) = ln(7x + 4) Reorder the terms: 2ln(1 + 3x) + -1ln(x + 1) = ln(7x + 4) (1 * 2ln + 3x * 2ln) + -1ln(x + 1) = ln(7x + 4) (2ln + 6lnx) + -1ln(x + 1) = ln(7x + 4) Reorder the terms: 2ln + 6lnx + -1ln(1 + x) = ln(7x + 4) 2ln + 6lnx + (1 * -1ln + x * -1ln) = ln(7x + 4) 2ln + 6lnx + (-1ln + -1lnx) = ln(7x + 4) Reorder the terms: 2ln + -1ln + 6lnx + -1lnx = ln(7x + 4) Combine like terms: 2ln + -1ln = 1ln 1ln + 6lnx + -1lnx = ln(7x + 4) Combine like terms: 6lnx + -1lnx = 5lnx 1ln + 5lnx = ln(7x + 4) Reorder the terms: 1ln + 5lnx = ln(4 + 7x) 1ln + 5lnx = (4 * ln + 7x * ln) 1ln + 5lnx = (4ln + 7lnx) Solving 1ln + 5lnx = 4ln + 7lnx 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. 1ln + -4ln + 5lnx = 4ln + -4ln + 7lnx Combine like terms: 1ln + -4ln = -3ln -3ln + 5lnx = 4ln + -4ln + 7lnx Combine like terms: 4ln + -4ln = 0 -3ln + 5lnx = 0 + 7lnx -3ln + 5lnx = 7lnx Add '-7lnx' to each side of the equation. -3ln + 5lnx + -7lnx = 7lnx + -7lnx Combine like terms: 5lnx + -7lnx = -2lnx -3ln + -2lnx = 7lnx + -7lnx Combine like terms: 7lnx + -7lnx = 0 -3ln + -2lnx = 0 Factor out the Greatest Common Factor (GCF), '-1ln'. -1ln(3 + 2x) = 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 '(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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