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Simplifying lnx2 + -1ln2 = ln(3x + -4) Reorder the terms: lnx2 + -1ln2 = ln(-4 + 3x) lnx2 + -1ln2 = (-4 * ln + 3x * ln) lnx2 + -1ln2 = (-4ln + 3lnx) Solving lnx2 + -1ln2 = -4ln + 3lnx 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. lnx2 + 4ln + -1ln2 = -4ln + 4ln + 3lnx Reorder the terms: 4ln + lnx2 + -1ln2 = -4ln + 4ln + 3lnx Combine like terms: -4ln + 4ln = 0 4ln + lnx2 + -1ln2 = 0 + 3lnx 4ln + lnx2 + -1ln2 = 3lnx Add '-3lnx' to each side of the equation. 4ln + lnx2 + -3lnx + -1ln2 = 3lnx + -3lnx Reorder the terms: 4ln + -3lnx + lnx2 + -1ln2 = 3lnx + -3lnx Combine like terms: 3lnx + -3lnx = 0 4ln + -3lnx + lnx2 + -1ln2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(4 + -3x + x2 + -1n) = 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 '(4 + -3x + x2 + -1n)' equal to zero and attempt to solve: Simplifying 4 + -3x + x2 + -1n = 0 Reorder the terms: 4 + -1n + -3x + x2 = 0 Solving 4 + -1n + -3x + x2 = 0 Move all terms containing l to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -1n + -3x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + -1n + -3x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1n + -3x + x2 = 0 + -4 -1n + -3x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 -1n + -3x + x2 = -4 Add 'n' to each side of the equation. -1n + -3x + n + x2 = -4 + n Reorder the terms: -1n + n + -3x + x2 = -4 + n Combine like terms: -1n + n = 0 0 + -3x + x2 = -4 + n -3x + x2 = -4 + n Add '3x' to each side of the equation. -3x + 3x + x2 = -4 + n + 3x Combine like terms: -3x + 3x = 0 0 + x2 = -4 + n + 3x x2 = -4 + n + 3x Add '-1x2' to each side of the equation. x2 + -1x2 = -4 + n + 3x + -1x2 Combine like terms: x2 + -1x2 = 0 0 = -4 + n + 3x + -1x2 Simplifying 0 = -4 + n + 3x + -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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