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