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Simplifying 8ln(5x + 4) + -1ln(2x + 4) = 0 Reorder the terms: 8ln(4 + 5x) + -1ln(2x + 4) = 0 (4 * 8ln + 5x * 8ln) + -1ln(2x + 4) = 0 (32ln + 40lnx) + -1ln(2x + 4) = 0 Reorder the terms: 32ln + 40lnx + -1ln(4 + 2x) = 0 32ln + 40lnx + (4 * -1ln + 2x * -1ln) = 0 32ln + 40lnx + (-4ln + -2lnx) = 0 Reorder the terms: 32ln + -4ln + 40lnx + -2lnx = 0 Combine like terms: 32ln + -4ln = 28ln 28ln + 40lnx + -2lnx = 0 Combine like terms: 40lnx + -2lnx = 38lnx 28ln + 38lnx = 0 Solving 28ln + 38lnx = 0 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(14 + 19x) = 0 Ignore the factor 2.Subproblem 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 '(14 + 19x)' equal to zero and attempt to solve: Simplifying 14 + 19x = 0 Solving 14 + 19x = 0 Move all terms containing l to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + 19x = 0 + -14 Combine like terms: 14 + -14 = 0 0 + 19x = 0 + -14 19x = 0 + -14 Combine like terms: 0 + -14 = -14 19x = -14 Add '-19x' to each side of the equation. 19x + -19x = -14 + -19x Combine like terms: 19x + -19x = 0 0 = -14 + -19x Simplifying 0 = -14 + -19x 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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