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Simplifying ln(x + -2) + ln(4x + 1) = 2ln(2x + -3) Reorder the terms: ln(-2 + x) + ln(4x + 1) = 2ln(2x + -3) (-2 * ln + x * ln) + ln(4x + 1) = 2ln(2x + -3) (-2ln + lnx) + ln(4x + 1) = 2ln(2x + -3) Reorder the terms: -2ln + lnx + ln(1 + 4x) = 2ln(2x + -3) -2ln + lnx + (1 * ln + 4x * ln) = 2ln(2x + -3) -2ln + lnx + (1ln + 4lnx) = 2ln(2x + -3) Reorder the terms: -2ln + 1ln + lnx + 4lnx = 2ln(2x + -3) Combine like terms: -2ln + 1ln = -1ln -1ln + lnx + 4lnx = 2ln(2x + -3) Combine like terms: lnx + 4lnx = 5lnx -1ln + 5lnx = 2ln(2x + -3) Reorder the terms: -1ln + 5lnx = 2ln(-3 + 2x) -1ln + 5lnx = (-3 * 2ln + 2x * 2ln) -1ln + 5lnx = (-6ln + 4lnx) Solving -1ln + 5lnx = -6ln + 4lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '6ln' to each side of the equation. -1ln + 6ln + 5lnx = -6ln + 6ln + 4lnx Combine like terms: -1ln + 6ln = 5ln 5ln + 5lnx = -6ln + 6ln + 4lnx Combine like terms: -6ln + 6ln = 0 5ln + 5lnx = 0 + 4lnx 5ln + 5lnx = 4lnx Add '-4lnx' to each side of the equation. 5ln + 5lnx + -4lnx = 4lnx + -4lnx Combine like terms: 5lnx + -4lnx = 1lnx 5ln + 1lnx = 4lnx + -4lnx Combine like terms: 4lnx + -4lnx = 0 5ln + 1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(5 + x) = 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 '(5 + x)' equal to zero and attempt to solve: Simplifying 5 + x = 0 Solving 5 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Add '-1x' to each side of the equation. x + -1x = -5 + -1x Combine like terms: x + -1x = 0 0 = -5 + -1x Simplifying 0 = -5 + -1x 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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