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