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Simplifying 2ln(x + -2) = ln(-2x + 52) Reorder the terms: 2ln(-2 + x) = ln(-2x + 52) (-2 * 2ln + x * 2ln) = ln(-2x + 52) (-4ln + 2lnx) = ln(-2x + 52) Reorder the terms: -4ln + 2lnx = ln(52 + -2x) -4ln + 2lnx = (52 * ln + -2x * ln) -4ln + 2lnx = (52ln + -2lnx) Solving -4ln + 2lnx = 52ln + -2lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-52ln' to each side of the equation. -4ln + -52ln + 2lnx = 52ln + -52ln + -2lnx Combine like terms: -4ln + -52ln = -56ln -56ln + 2lnx = 52ln + -52ln + -2lnx Combine like terms: 52ln + -52ln = 0 -56ln + 2lnx = 0 + -2lnx -56ln + 2lnx = -2lnx Add '2lnx' to each side of the equation. -56ln + 2lnx + 2lnx = -2lnx + 2lnx Combine like terms: 2lnx + 2lnx = 4lnx -56ln + 4lnx = -2lnx + 2lnx Combine like terms: -2lnx + 2lnx = 0 -56ln + 4lnx = 0 Factor out the Greatest Common Factor (GCF), '4ln'. 4ln(-14 + 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 '(-14 + x)' equal to zero and attempt to solve: Simplifying -14 + x = 0 Solving -14 + x = 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 + x = 0 + 14 Combine like terms: -14 + 14 = 0 0 + x = 0 + 14 x = 0 + 14 Combine like terms: 0 + 14 = 14 x = 14 Add '-1x' to each side of the equation. x + -1x = 14 + -1x Combine like terms: x + -1x = 0 0 = 14 + -1x Simplifying 0 = 14 + -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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