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Simplifying -1ln(3x + 1) + -5 = ln(x + 4) Reorder the terms: -1ln(1 + 3x) + -5 = ln(x + 4) (1 * -1ln + 3x * -1ln) + -5 = ln(x + 4) (-1ln + -3lnx) + -5 = ln(x + 4) Reorder the terms: -5 + -1ln + -3lnx = ln(x + 4) Reorder the terms: -5 + -1ln + -3lnx = ln(4 + x) -5 + -1ln + -3lnx = (4 * ln + x * ln) -5 + -1ln + -3lnx = (4ln + lnx) Solving -5 + -1ln + -3lnx = 4ln + lnx 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. -5 + -1ln + -4ln + -3lnx = 4ln + -4ln + lnx Combine like terms: -1ln + -4ln = -5ln -5 + -5ln + -3lnx = 4ln + -4ln + lnx Combine like terms: 4ln + -4ln = 0 -5 + -5ln + -3lnx = 0 + lnx -5 + -5ln + -3lnx = lnx Add '-1lnx' to each side of the equation. -5 + -5ln + -3lnx + -1lnx = lnx + -1lnx Combine like terms: -3lnx + -1lnx = -4lnx -5 + -5ln + -4lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -5 + -5ln + -4lnx = 0 Add '5' to each side of the equation. -5 + -5ln + 5 + -4lnx = 0 + 5 Reorder the terms: -5 + 5 + -5ln + -4lnx = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -5ln + -4lnx = 0 + 5 -5ln + -4lnx = 0 + 5 Combine like terms: 0 + 5 = 5 -5ln + -4lnx = 5 Reorder the terms: -5 + -5ln + -4lnx = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + -5ln + -4lnx = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(5 + 5ln + 4lnx) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(5 + 5ln + 4lnx)' equal to zero and attempt to solve: Simplifying 5 + 5ln + 4lnx = 0 Solving 5 + 5ln + 4lnx = 0 Move all terms containing l to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + 5ln + -5 + 4lnx = 0 + -5 Reorder the terms: 5 + -5 + 5ln + 4lnx = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 5ln + 4lnx = 0 + -5 5ln + 4lnx = 0 + -5 Combine like terms: 0 + -5 = -5 5ln + 4lnx = -5 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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