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Simplifying lnx + ln(x + 2) = ln(4 + -5x) Reorder the terms: lnx + ln(2 + x) = ln(4 + -5x) lnx + (2 * ln + x * ln) = ln(4 + -5x) lnx + (2ln + lnx) = ln(4 + -5x) Reorder the terms: 2ln + lnx + lnx = ln(4 + -5x) Combine like terms: lnx + lnx = 2lnx 2ln + 2lnx = ln(4 + -5x) 2ln + 2lnx = (4 * ln + -5x * ln) 2ln + 2lnx = (4ln + -5lnx) Solving 2ln + 2lnx = 4ln + -5lnx 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. 2ln + -4ln + 2lnx = 4ln + -4ln + -5lnx Combine like terms: 2ln + -4ln = -2ln -2ln + 2lnx = 4ln + -4ln + -5lnx Combine like terms: 4ln + -4ln = 0 -2ln + 2lnx = 0 + -5lnx -2ln + 2lnx = -5lnx Add '5lnx' to each side of the equation. -2ln + 2lnx + 5lnx = -5lnx + 5lnx Combine like terms: 2lnx + 5lnx = 7lnx -2ln + 7lnx = -5lnx + 5lnx Combine like terms: -5lnx + 5lnx = 0 -2ln + 7lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-2 + 7x) = 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 '(-2 + 7x)' equal to zero and attempt to solve: Simplifying -2 + 7x = 0 Solving -2 + 7x = 0 Move all terms containing l to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + 7x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 7x = 0 + 2 7x = 0 + 2 Combine like terms: 0 + 2 = 2 7x = 2 Add '-7x' to each side of the equation. 7x + -7x = 2 + -7x Combine like terms: 7x + -7x = 0 0 = 2 + -7x Simplifying 0 = 2 + -7x 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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