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Simplifying ln(2X + -7X + 5) = ln(2X + -9) Reorder the terms: ln(5 + 2X + -7X) = ln(2X + -9) Combine like terms: 2X + -7X = -5X ln(5 + -5X) = ln(2X + -9) (5 * ln + -5X * ln) = ln(2X + -9) (5ln + -5lnX) = ln(2X + -9) Reorder the terms: 5ln + -5lnX = ln(-9 + 2X) 5ln + -5lnX = (-9 * ln + 2X * ln) 5ln + -5lnX = (-9ln + 2lnX) Solving 5ln + -5lnX = -9ln + 2lnX Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '9ln' to each side of the equation. 5ln + 9ln + -5lnX = -9ln + 9ln + 2lnX Combine like terms: 5ln + 9ln = 14ln 14ln + -5lnX = -9ln + 9ln + 2lnX Combine like terms: -9ln + 9ln = 0 14ln + -5lnX = 0 + 2lnX 14ln + -5lnX = 2lnX Add '-2lnX' to each side of the equation. 14ln + -5lnX + -2lnX = 2lnX + -2lnX Combine like terms: -5lnX + -2lnX = -7lnX 14ln + -7lnX = 2lnX + -2lnX Combine like terms: 2lnX + -2lnX = 0 14ln + -7lnX = 0 Factor out the Greatest Common Factor (GCF), '7ln'. 7ln(2 + -1X) = 0 Ignore the factor 7.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 + -1X)' equal to zero and attempt to solve: Simplifying 2 + -1X = 0 Solving 2 + -1X = 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 + -1X = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1X = 0 + -2 -1X = 0 + -2 Combine like terms: 0 + -2 = -2 -1X = -2 Add 'X' to each side of the equation. -1X + X = -2 + X Combine like terms: -1X + X = 0 0 = -2 + X Simplifying 0 = -2 + 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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