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Simplifying 2ln(x) = ln(4x + -6) + -1ln(2) Multiply ln * x 2lnx = ln(4x + -6) + -1ln(2) Reorder the terms: 2lnx = ln(-6 + 4x) + -1ln(2) 2lnx = (-6 * ln + 4x * ln) + -1ln(2) 2lnx = (-6ln + 4lnx) + -1ln(2) Reorder the terms for easier multiplication: 2lnx = -6ln + 4lnx + -1 * 2ln Multiply -1 * 2 2lnx = -6ln + 4lnx + -2ln Reorder the terms: 2lnx = -6ln + -2ln + 4lnx Combine like terms: -6ln + -2ln = -8ln 2lnx = -8ln + 4lnx Solving 2lnx = -8ln + 4lnx 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. 8ln + 2lnx = -8ln + 8ln + 4lnx Combine like terms: -8ln + 8ln = 0 8ln + 2lnx = 0 + 4lnx 8ln + 2lnx = 4lnx Add '-4lnx' to each side of the equation. 8ln + 2lnx + -4lnx = 4lnx + -4lnx Combine like terms: 2lnx + -4lnx = -2lnx 8ln + -2lnx = 4lnx + -4lnx Combine like terms: 4lnx + -4lnx = 0 8ln + -2lnx = 0 Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(4 + -1x) = 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 '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Add 'x' to each side of the equation. -1x + x = -4 + x Combine like terms: -1x + x = 0 0 = -4 + x Simplifying 0 = -4 + 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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