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Simplifying ln(4x + 3) = 2ln(4x + -3) Reorder the terms: ln(3 + 4x) = 2ln(4x + -3) (3 * ln + 4x * ln) = 2ln(4x + -3) (3ln + 4lnx) = 2ln(4x + -3) Reorder the terms: 3ln + 4lnx = 2ln(-3 + 4x) 3ln + 4lnx = (-3 * 2ln + 4x * 2ln) 3ln + 4lnx = (-6ln + 8lnx) Solving 3ln + 4lnx = -6ln + 8lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '6ln' to each side of the equation. 3ln + 6ln + 4lnx = -6ln + 6ln + 8lnx Combine like terms: 3ln + 6ln = 9ln 9ln + 4lnx = -6ln + 6ln + 8lnx Combine like terms: -6ln + 6ln = 0 9ln + 4lnx = 0 + 8lnx 9ln + 4lnx = 8lnx Add '-8lnx' to each side of the equation. 9ln + 4lnx + -8lnx = 8lnx + -8lnx Combine like terms: 4lnx + -8lnx = -4lnx 9ln + -4lnx = 8lnx + -8lnx Combine like terms: 8lnx + -8lnx = 0 9ln + -4lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(9 + -4x) = 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 '(9 + -4x)' equal to zero and attempt to solve: Simplifying 9 + -4x = 0 Solving 9 + -4x = 0 Move all terms containing l to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -4x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -4x = 0 + -9 -4x = 0 + -9 Combine like terms: 0 + -9 = -9 -4x = -9 Add '4x' to each side of the equation. -4x + 4x = -9 + 4x Combine like terms: -4x + 4x = 0 0 = -9 + 4x Simplifying 0 = -9 + 4x 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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