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Simplifying ln(2x + -1) + ln(2x + 1) = ln(5x + -2) Reorder the terms: ln(-1 + 2x) + ln(2x + 1) = ln(5x + -2) (-1 * ln + 2x * ln) + ln(2x + 1) = ln(5x + -2) (-1ln + 2lnx) + ln(2x + 1) = ln(5x + -2) Reorder the terms: -1ln + 2lnx + ln(1 + 2x) = ln(5x + -2) -1ln + 2lnx + (1 * ln + 2x * ln) = ln(5x + -2) -1ln + 2lnx + (1ln + 2lnx) = ln(5x + -2) Reorder the terms: -1ln + 1ln + 2lnx + 2lnx = ln(5x + -2) Combine like terms: -1ln + 1ln = 0 0 + 2lnx + 2lnx = ln(5x + -2) 2lnx + 2lnx = ln(5x + -2) Combine like terms: 2lnx + 2lnx = 4lnx 4lnx = ln(5x + -2) Reorder the terms: 4lnx = ln(-2 + 5x) 4lnx = (-2 * ln + 5x * ln) 4lnx = (-2ln + 5lnx) Solving 4lnx = -2ln + 5lnx 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 + 5lnx Combine like terms: -2ln + 2ln = 0 2ln + 4lnx = 0 + 5lnx 2ln + 4lnx = 5lnx Add '-5lnx' to each side of the equation. 2ln + 4lnx + -5lnx = 5lnx + -5lnx Combine like terms: 4lnx + -5lnx = -1lnx 2ln + -1lnx = 5lnx + -5lnx Combine like terms: 5lnx + -5lnx = 0 2ln + -1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(2 + -1x) = 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. The solution to this equation could not be determined.
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