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Simplifying 2ln(x + -2) = ln(-4x + 40) Reorder the terms: 2ln(-2 + x) = ln(-4x + 40) (-2 * 2ln + x * 2ln) = ln(-4x + 40) (-4ln + 2lnx) = ln(-4x + 40) Reorder the terms: -4ln + 2lnx = ln(40 + -4x) -4ln + 2lnx = (40 * ln + -4x * ln) -4ln + 2lnx = (40ln + -4lnx) Solving -4ln + 2lnx = 40ln + -4lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-40ln' to each side of the equation. -4ln + -40ln + 2lnx = 40ln + -40ln + -4lnx Combine like terms: -4ln + -40ln = -44ln -44ln + 2lnx = 40ln + -40ln + -4lnx Combine like terms: 40ln + -40ln = 0 -44ln + 2lnx = 0 + -4lnx -44ln + 2lnx = -4lnx Add '4lnx' to each side of the equation. -44ln + 2lnx + 4lnx = -4lnx + 4lnx Combine like terms: 2lnx + 4lnx = 6lnx -44ln + 6lnx = -4lnx + 4lnx Combine like terms: -4lnx + 4lnx = 0 -44ln + 6lnx = 0 Factor out the Greatest Common Factor (GCF), '2ln'. 2ln(-22 + 3x) = 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 '(-22 + 3x)' equal to zero and attempt to solve: Simplifying -22 + 3x = 0 Solving -22 + 3x = 0 Move all terms containing l to the left, all other terms to the right. Add '22' to each side of the equation. -22 + 22 + 3x = 0 + 22 Combine like terms: -22 + 22 = 0 0 + 3x = 0 + 22 3x = 0 + 22 Combine like terms: 0 + 22 = 22 3x = 22 Add '-3x' to each side of the equation. 3x + -3x = 22 + -3x Combine like terms: 3x + -3x = 0 0 = 22 + -3x Simplifying 0 = 22 + -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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