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Simplifying 2lnX = ln(12 + -1X) 2lnX = (12 * ln + -1X * ln) 2lnX = (12ln + -1lnX) Solving 2lnX = 12ln + -1lnX Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-12ln' to each side of the equation. -12ln + 2lnX = 12ln + -12ln + -1lnX Combine like terms: 12ln + -12ln = 0 -12ln + 2lnX = 0 + -1lnX -12ln + 2lnX = -1lnX Add 'lnX' to each side of the equation. -12ln + 2lnX + lnX = -1lnX + lnX Combine like terms: 2lnX + lnX = 3lnX -12ln + 3lnX = -1lnX + lnX Combine like terms: -1lnX + lnX = 0 -12ln + 3lnX = 0 Factor out the Greatest Common Factor (GCF), '3ln'. 3ln(-4 + X) = 0 Ignore the factor 3.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 + X)' equal to zero and attempt to solve: Simplifying -4 + X = 0 Solving -4 + X = 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 + X = 0 + 4 Combine like terms: -4 + 4 = 0 0 + X = 0 + 4 X = 0 + 4 Combine like terms: 0 + 4 = 4 X = 4 Add '-1X' to each side of the equation. X + -1X = 4 + -1X Combine like terms: X + -1X = 0 0 = 4 + -1X Simplifying 0 = 4 + -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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