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