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Simplifying ln(-5x + 1) = ln(6x + -2) Reorder the terms: ln(1 + -5x) = ln(6x + -2) (1 * ln + -5x * ln) = ln(6x + -2) (1ln + -5lnx) = ln(6x + -2) Reorder the terms: 1ln + -5lnx = ln(-2 + 6x) 1ln + -5lnx = (-2 * ln + 6x * ln) 1ln + -5lnx = (-2ln + 6lnx) Solving 1ln + -5lnx = -2ln + 6lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '2ln' to each side of the equation. 1ln + 2ln + -5lnx = -2ln + 2ln + 6lnx Combine like terms: 1ln + 2ln = 3ln 3ln + -5lnx = -2ln + 2ln + 6lnx Combine like terms: -2ln + 2ln = 0 3ln + -5lnx = 0 + 6lnx 3ln + -5lnx = 6lnx Add '-6lnx' to each side of the equation. 3ln + -5lnx + -6lnx = 6lnx + -6lnx Combine like terms: -5lnx + -6lnx = -11lnx 3ln + -11lnx = 6lnx + -6lnx Combine like terms: 6lnx + -6lnx = 0 3ln + -11lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(3 + -11x) = 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 '(3 + -11x)' equal to zero and attempt to solve: Simplifying 3 + -11x = 0 Solving 3 + -11x = 0 Move all terms containing l to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -11x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -11x = 0 + -3 -11x = 0 + -3 Combine like terms: 0 + -3 = -3 -11x = -3 Add '11x' to each side of the equation. -11x + 11x = -3 + 11x Combine like terms: -11x + 11x = 0 0 = -3 + 11x Simplifying 0 = -3 + 11x 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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