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Simplifying ln(x2 + 5x + 4) + -1ln(x + 4) = ln(5x + -7) Reorder the terms: ln(4 + 5x + x2) + -1ln(x + 4) = ln(5x + -7) (4 * ln + 5x * ln + x2 * ln) + -1ln(x + 4) = ln(5x + -7) (4ln + 5lnx + lnx2) + -1ln(x + 4) = ln(5x + -7) Reorder the terms: 4ln + 5lnx + lnx2 + -1ln(4 + x) = ln(5x + -7) 4ln + 5lnx + lnx2 + (4 * -1ln + x * -1ln) = ln(5x + -7) 4ln + 5lnx + lnx2 + (-4ln + -1lnx) = ln(5x + -7) Reorder the terms: 4ln + -4ln + 5lnx + -1lnx + lnx2 = ln(5x + -7) Combine like terms: 4ln + -4ln = 0 0 + 5lnx + -1lnx + lnx2 = ln(5x + -7) 5lnx + -1lnx + lnx2 = ln(5x + -7) Combine like terms: 5lnx + -1lnx = 4lnx 4lnx + lnx2 = ln(5x + -7) Reorder the terms: 4lnx + lnx2 = ln(-7 + 5x) 4lnx + lnx2 = (-7 * ln + 5x * ln) 4lnx + lnx2 = (-7ln + 5lnx) Solving 4lnx + lnx2 = -7ln + 5lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '7ln' to each side of the equation. 4lnx + 7ln + lnx2 = -7ln + 7ln + 5lnx Reorder the terms: 7ln + 4lnx + lnx2 = -7ln + 7ln + 5lnx Combine like terms: -7ln + 7ln = 0 7ln + 4lnx + lnx2 = 0 + 5lnx 7ln + 4lnx + lnx2 = 5lnx Add '-5lnx' to each side of the equation. 7ln + 4lnx + -5lnx + lnx2 = 5lnx + -5lnx Combine like terms: 4lnx + -5lnx = -1lnx 7ln + -1lnx + lnx2 = 5lnx + -5lnx Combine like terms: 5lnx + -5lnx = 0 7ln + -1lnx + lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(7 + -1x + x2) = 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 + -1x + x2)' equal to zero and attempt to solve: Simplifying 7 + -1x + x2 = 0 Solving 7 + -1x + x2 = 0 Move all terms containing l to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -1x + -7 + x2 = 0 + -7 Reorder the terms: 7 + -7 + -1x + x2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x + x2 = 0 + -7 -1x + x2 = 0 + -7 Combine like terms: 0 + -7 = -7 -1x + x2 = -7 Add 'x' to each side of the equation. -1x + x + x2 = -7 + x Combine like terms: -1x + x = 0 0 + x2 = -7 + x x2 = -7 + x Add '-1x2' to each side of the equation. x2 + -1x2 = -7 + x + -1x2 Combine like terms: x2 + -1x2 = 0 0 = -7 + x + -1x2 Simplifying 0 = -7 + x + -1x2 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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