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Simplifying 2ln(x + -5) = ln(3x + -11) Reorder the terms: 2ln(-5 + x) = ln(3x + -11) (-5 * 2ln + x * 2ln) = ln(3x + -11) (-10ln + 2lnx) = ln(3x + -11) Reorder the terms: -10ln + 2lnx = ln(-11 + 3x) -10ln + 2lnx = (-11 * ln + 3x * ln) -10ln + 2lnx = (-11ln + 3lnx) Solving -10ln + 2lnx = -11ln + 3lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '11ln' to each side of the equation. -10ln + 11ln + 2lnx = -11ln + 11ln + 3lnx Combine like terms: -10ln + 11ln = 1ln 1ln + 2lnx = -11ln + 11ln + 3lnx Combine like terms: -11ln + 11ln = 0 1ln + 2lnx = 0 + 3lnx 1ln + 2lnx = 3lnx Add '-3lnx' to each side of the equation. 1ln + 2lnx + -3lnx = 3lnx + -3lnx Combine like terms: 2lnx + -3lnx = -1lnx 1ln + -1lnx = 3lnx + -3lnx Combine like terms: 3lnx + -3lnx = 0 1ln + -1lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(1 + -1x) = 0Subproblem 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 '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Add 'x' to each side of the equation. -1x + x = -1 + x Combine like terms: -1x + x = 0 0 = -1 + x Simplifying 0 = -1 + 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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