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Simplifying ln(2x + -1) + ln(2x + 1) = ln(x + 2) Reorder the terms: ln(-1 + 2x) + ln(2x + 1) = ln(x + 2) (-1 * ln + 2x * ln) + ln(2x + 1) = ln(x + 2) (-1ln + 2lnx) + ln(2x + 1) = ln(x + 2) Reorder the terms: -1ln + 2lnx + ln(1 + 2x) = ln(x + 2) -1ln + 2lnx + (1 * ln + 2x * ln) = ln(x + 2) -1ln + 2lnx + (1ln + 2lnx) = ln(x + 2) Reorder the terms: -1ln + 1ln + 2lnx + 2lnx = ln(x + 2) Combine like terms: -1ln + 1ln = 0 0 + 2lnx + 2lnx = ln(x + 2) 2lnx + 2lnx = ln(x + 2) Combine like terms: 2lnx + 2lnx = 4lnx 4lnx = ln(x + 2) Reorder the terms: 4lnx = ln(2 + x) 4lnx = (2 * ln + x * ln) 4lnx = (2ln + lnx) Solving 4lnx = 2ln + lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-2ln' to each side of the equation. -2ln + 4lnx = 2ln + -2ln + lnx Combine like terms: 2ln + -2ln = 0 -2ln + 4lnx = 0 + lnx -2ln + 4lnx = lnx Add '-1lnx' to each side of the equation. -2ln + 4lnx + -1lnx = lnx + -1lnx Combine like terms: 4lnx + -1lnx = 3lnx -2ln + 3lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -2ln + 3lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-2 + 3x) = 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 + 3x)' equal to zero and attempt to solve: Simplifying -2 + 3x = 0 Solving -2 + 3x = 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 + 3x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 3x = 0 + 2 3x = 0 + 2 Combine like terms: 0 + 2 = 2 3x = 2 Add '-3x' to each side of the equation. 3x + -3x = 2 + -3x Combine like terms: 3x + -3x = 0 0 = 2 + -3x Simplifying 0 = 2 + -3x 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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