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Simplifying 2ln(2) + ln(x2 + -1) = ln(4x) Reorder the terms for easier multiplication: 2 * 2ln + ln(x2 + -1) = ln(4x) Multiply 2 * 2 4ln + ln(x2 + -1) = ln(4x) Reorder the terms: 4ln + ln(-1 + x2) = ln(4x) 4ln + (-1 * ln + x2 * ln) = ln(4x) 4ln + (-1ln + lnx2) = ln(4x) Combine like terms: 4ln + -1ln = 3ln 3ln + lnx2 = ln(4x) Remove parenthesis around (4x) 3ln + lnx2 = ln * 4x Reorder the terms for easier multiplication: 3ln + lnx2 = 4ln * x Multiply ln * x 3ln + lnx2 = 4lnx Solving 3ln + lnx2 = 4lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-4lnx' to each side of the equation. 3ln + -4lnx + lnx2 = 4lnx + -4lnx Combine like terms: 4lnx + -4lnx = 0 3ln + -4lnx + lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(3 + -4x + x2) = 0 Factor a trinomial. ln((1 + -1x)(3 + -1x)) = 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 '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Add 'x' to each side of the equation. -1x + x = -1 + x Combine like terms: -1x + x = 0 0 = -1 + x Simplifying 0 = -1 + x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Add 'x' to each side of the equation. -1x + x = -3 + x Combine like terms: -1x + x = 0 0 = -3 + x Simplifying 0 = -3 + x 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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