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