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Simplifying ln(3x + -2) + ln(2x) = ln(6x2 + -8) Reorder the terms: ln(-2 + 3x) + ln(2x) = ln(6x2 + -8) (-2 * ln + 3x * ln) + ln(2x) = ln(6x2 + -8) (-2ln + 3lnx) + ln(2x) = ln(6x2 + -8) Remove parenthesis around (2x) -2ln + 3lnx + ln * 2x = ln(6x2 + -8) Reorder the terms for easier multiplication: -2ln + 3lnx + 2ln * x = ln(6x2 + -8) Multiply ln * x -2ln + 3lnx + 2lnx = ln(6x2 + -8) Combine like terms: 3lnx + 2lnx = 5lnx -2ln + 5lnx = ln(6x2 + -8) Reorder the terms: -2ln + 5lnx = ln(-8 + 6x2) -2ln + 5lnx = (-8 * ln + 6x2 * ln) -2ln + 5lnx = (-8ln + 6lnx2) Solving -2ln + 5lnx = -8ln + 6lnx2 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '8ln' to each side of the equation. -2ln + 8ln + 5lnx = -8ln + 8ln + 6lnx2 Combine like terms: -2ln + 8ln = 6ln 6ln + 5lnx = -8ln + 8ln + 6lnx2 Combine like terms: -8ln + 8ln = 0 6ln + 5lnx = 0 + 6lnx2 6ln + 5lnx = 6lnx2 Add '-6lnx2' to each side of the equation. 6ln + 5lnx + -6lnx2 = 6lnx2 + -6lnx2 Combine like terms: 6lnx2 + -6lnx2 = 0 6ln + 5lnx + -6lnx2 = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(6 + 5x + -6x2) = 0 Factor a trinomial. ln((3 + -2x)(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 '(3 + -2x)' equal to zero and attempt to solve: Simplifying 3 + -2x = 0 Solving 3 + -2x = 0 Move all terms containing l to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2x = 0 + -3 -2x = 0 + -3 Combine like terms: 0 + -3 = -3 -2x = -3 Add '2x' to each side of the equation. -2x + 2x = -3 + 2x Combine like terms: -2x + 2x = 0 0 = -3 + 2x Simplifying 0 = -3 + 2x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
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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