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Simplifying 2ln(x + -1) = ln(-4x + 25) Reorder the terms: 2ln(-1 + x) = ln(-4x + 25) (-1 * 2ln + x * 2ln) = ln(-4x + 25) (-2ln + 2lnx) = ln(-4x + 25) Reorder the terms: -2ln + 2lnx = ln(25 + -4x) -2ln + 2lnx = (25 * ln + -4x * ln) -2ln + 2lnx = (25ln + -4lnx) Solving -2ln + 2lnx = 25ln + -4lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-25ln' to each side of the equation. -2ln + -25ln + 2lnx = 25ln + -25ln + -4lnx Combine like terms: -2ln + -25ln = -27ln -27ln + 2lnx = 25ln + -25ln + -4lnx Combine like terms: 25ln + -25ln = 0 -27ln + 2lnx = 0 + -4lnx -27ln + 2lnx = -4lnx Add '4lnx' to each side of the equation. -27ln + 2lnx + 4lnx = -4lnx + 4lnx Combine like terms: 2lnx + 4lnx = 6lnx -27ln + 6lnx = -4lnx + 4lnx Combine like terms: -4lnx + 4lnx = 0 -27ln + 6lnx = 0 Factor out the Greatest Common Factor (GCF), '3ln'. 3ln(-9 + 2x) = 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 '(-9 + 2x)' equal to zero and attempt to solve: Simplifying -9 + 2x = 0 Solving -9 + 2x = 0 Move all terms containing l to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + 2x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 2x = 0 + 9 2x = 0 + 9 Combine like terms: 0 + 9 = 9 2x = 9 Add '-2x' to each side of the equation. 2x + -2x = 9 + -2x Combine like terms: 2x + -2x = 0 0 = 9 + -2x Simplifying 0 = 9 + -2x 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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