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