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Simplifying 2ln(x + 1) = ln(2x2) + -1ln(x) Reorder the terms: 2ln(1 + x) = ln(2x2) + -1ln(x) (1 * 2ln + x * 2ln) = ln(2x2) + -1ln(x) (2ln + 2lnx) = ln(2x2) + -1ln(x) Remove parenthesis around (2x2) 2ln + 2lnx = ln * 2x2 + -1ln(x) Reorder the terms for easier multiplication: 2ln + 2lnx = 2ln * x2 + -1ln(x) Multiply ln * x2 2ln + 2lnx = 2lnx2 + -1ln(x) Multiply ln * x 2ln + 2lnx = 2lnx2 + -1lnx Reorder the terms: 2ln + 2lnx = -1lnx + 2lnx2 Solving 2ln + 2lnx = -1lnx + 2lnx2 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add 'lnx' to each side of the equation. 2ln + 2lnx + lnx = -1lnx + lnx + 2lnx2 Combine like terms: 2lnx + lnx = 3lnx 2ln + 3lnx = -1lnx + lnx + 2lnx2 Combine like terms: -1lnx + lnx = 0 2ln + 3lnx = 0 + 2lnx2 2ln + 3lnx = 2lnx2 Add '-2lnx2' to each side of the equation. 2ln + 3lnx + -2lnx2 = 2lnx2 + -2lnx2 Combine like terms: 2lnx2 + -2lnx2 = 0 2ln + 3lnx + -2lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(2 + 3x + -2x2) = 0 Factor a trinomial. ln((2 + -1x)(1 + 2x)) = 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 '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Add 'x' to each side of the equation. -1x + x = -2 + x Combine like terms: -1x + x = 0 0 = -2 + x Simplifying 0 = -2 + 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 '(1 + 2x)' equal to zero and attempt to solve: Simplifying 1 + 2x = 0 Solving 1 + 2x = 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 + 2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2x = 0 + -1 2x = 0 + -1 Combine like terms: 0 + -1 = -1 2x = -1 Add '-2x' to each side of the equation. 2x + -2x = -1 + -2x Combine like terms: 2x + -2x = 0 0 = -1 + -2x Simplifying 0 = -1 + -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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