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Simplifying ln(3x + -1) + -1ln(2 + x) = ln2 Reorder the terms: ln(-1 + 3x) + -1ln(2 + x) = ln2 (-1 * ln + 3x * ln) + -1ln(2 + x) = ln2 (-1ln + 3lnx) + -1ln(2 + x) = ln2 -1ln + 3lnx + (2 * -1ln + x * -1ln) = ln2 -1ln + 3lnx + (-2ln + -1lnx) = ln2 Reorder the terms: -1ln + -2ln + 3lnx + -1lnx = ln2 Combine like terms: -1ln + -2ln = -3ln -3ln + 3lnx + -1lnx = ln2 Combine like terms: 3lnx + -1lnx = 2lnx -3ln + 2lnx = ln2 Solving -3ln + 2lnx = ln2 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-1ln2' to each side of the equation. -3ln + 2lnx + -1ln2 = ln2 + -1ln2 Combine like terms: ln2 + -1ln2 = 0 -3ln + 2lnx + -1ln2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-3 + 2x + -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 '(-3 + 2x + -1n)' equal to zero and attempt to solve: Simplifying -3 + 2x + -1n = 0 Reorder the terms: -3 + -1n + 2x = 0 Solving -3 + -1n + 2x = 0 Move all terms containing l to the left, all other terms to the right. Add '3' to each side of the equation. -3 + -1n + 3 + 2x = 0 + 3 Reorder the terms: -3 + 3 + -1n + 2x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1n + 2x = 0 + 3 -1n + 2x = 0 + 3 Combine like terms: 0 + 3 = 3 -1n + 2x = 3 Add 'n' to each side of the equation. -1n + n + 2x = 3 + n Combine like terms: -1n + n = 0 0 + 2x = 3 + n 2x = 3 + n Add '-2x' to each side of the equation. 2x + -2x = 3 + n + -2x Combine like terms: 2x + -2x = 0 0 = 3 + n + -2x Simplifying 0 = 3 + n + -2x 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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