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Simplifying 2ln(x + -1) = ln(5x + 11) Reorder the terms: 2ln(-1 + x) = ln(5x + 11) (-1 * 2ln + x * 2ln) = ln(5x + 11) (-2ln + 2lnx) = ln(5x + 11) Reorder the terms: -2ln + 2lnx = ln(11 + 5x) -2ln + 2lnx = (11 * ln + 5x * ln) -2ln + 2lnx = (11ln + 5lnx) Solving -2ln + 2lnx = 11ln + 5lnx 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. -2ln + -11ln + 2lnx = 11ln + -11ln + 5lnx Combine like terms: -2ln + -11ln = -13ln -13ln + 2lnx = 11ln + -11ln + 5lnx Combine like terms: 11ln + -11ln = 0 -13ln + 2lnx = 0 + 5lnx -13ln + 2lnx = 5lnx Add '-5lnx' to each side of the equation. -13ln + 2lnx + -5lnx = 5lnx + -5lnx Combine like terms: 2lnx + -5lnx = -3lnx -13ln + -3lnx = 5lnx + -5lnx Combine like terms: 5lnx + -5lnx = 0 -13ln + -3lnx = 0 Factor out the Greatest Common Factor (GCF), '-1ln'. -1ln(13 + 3x) = 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 '(13 + 3x)' equal to zero and attempt to solve: Simplifying 13 + 3x = 0 Solving 13 + 3x = 0 Move all terms containing l to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + 3x = 0 + -13 Combine like terms: 13 + -13 = 0 0 + 3x = 0 + -13 3x = 0 + -13 Combine like terms: 0 + -13 = -13 3x = -13 Add '-3x' to each side of the equation. 3x + -3x = -13 + -3x Combine like terms: 3x + -3x = 0 0 = -13 + -3x Simplifying 0 = -13 + -3x 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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