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Simplifying ln(3x + 1) + -1ln(4 + -1x) = ln(4) Reorder the terms: ln(1 + 3x) + -1ln(4 + -1x) = ln(4) (1 * ln + 3x * ln) + -1ln(4 + -1x) = ln(4) (1ln + 3lnx) + -1ln(4 + -1x) = ln(4) 1ln + 3lnx + (4 * -1ln + -1x * -1ln) = ln(4) 1ln + 3lnx + (-4ln + 1lnx) = ln(4) Reorder the terms: 1ln + -4ln + 3lnx + 1lnx = ln(4) Combine like terms: 1ln + -4ln = -3ln -3ln + 3lnx + 1lnx = ln(4) Combine like terms: 3lnx + 1lnx = 4lnx -3ln + 4lnx = ln(4) Reorder the terms for easier multiplication: -3ln + 4lnx = 4ln Solving -3ln + 4lnx = 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 + 4lnx = 4ln + -4ln Combine like terms: -3ln + -4ln = -7ln -7ln + 4lnx = 4ln + -4ln Combine like terms: 4ln + -4ln = 0 -7ln + 4lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-7 + 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 '(-7 + 4x)' equal to zero and attempt to solve: Simplifying -7 + 4x = 0 Solving -7 + 4x = 0 Move all terms containing l to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + 4x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 4x = 0 + 7 4x = 0 + 7 Combine like terms: 0 + 7 = 7 4x = 7 Add '-4x' to each side of the equation. 4x + -4x = 7 + -4x Combine like terms: 4x + -4x = 0 0 = 7 + -4x Simplifying 0 = 7 + -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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