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Simplifying ln((2x2) + x) = 2ln(x + 2) Reorder the terms: ln(x + (2x2)) = 2ln(x + 2) (x * ln + (2x2) * ln) = 2ln(x + 2) (lnx + 2lnx2) = 2ln(x + 2) Reorder the terms: lnx + 2lnx2 = 2ln(2 + x) lnx + 2lnx2 = (2 * 2ln + x * 2ln) lnx + 2lnx2 = (4ln + 2lnx) Solving lnx + 2lnx2 = 4ln + 2lnx 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. lnx + -4ln + 2lnx2 = 4ln + -4ln + 2lnx Reorder the terms: -4ln + lnx + 2lnx2 = 4ln + -4ln + 2lnx Combine like terms: 4ln + -4ln = 0 -4ln + lnx + 2lnx2 = 0 + 2lnx -4ln + lnx + 2lnx2 = 2lnx Add '-2lnx' to each side of the equation. -4ln + lnx + -2lnx + 2lnx2 = 2lnx + -2lnx Combine like terms: lnx + -2lnx = -1lnx -4ln + -1lnx + 2lnx2 = 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 -4ln + -1lnx + 2lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-4 + -1x + 2x2) = 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 + -1x + 2x2)' equal to zero and attempt to solve: Simplifying -4 + -1x + 2x2 = 0 Solving -4 + -1x + 2x2 = 0 Move all terms containing l to the left, all other terms to the right. Add '4' to each side of the equation. -4 + -1x + 4 + 2x2 = 0 + 4 Reorder the terms: -4 + 4 + -1x + 2x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1x + 2x2 = 0 + 4 -1x + 2x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -1x + 2x2 = 4 Add 'x' to each side of the equation. -1x + x + 2x2 = 4 + x Combine like terms: -1x + x = 0 0 + 2x2 = 4 + x 2x2 = 4 + x Add '-2x2' to each side of the equation. 2x2 + -2x2 = 4 + x + -2x2 Combine like terms: 2x2 + -2x2 = 0 0 = 4 + x + -2x2 Simplifying 0 = 4 + x + -2x2 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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