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Simplifying ln(13x + -11) + -1ln(x + -2) + -1ln(x + 1) = ln(12) + -1ln(x + -1) Reorder the terms: ln(-11 + 13x) + -1ln(x + -2) + -1ln(x + 1) = ln(12) + -1ln(x + -1) (-11 * ln + 13x * ln) + -1ln(x + -2) + -1ln(x + 1) = ln(12) + -1ln(x + -1) (-11ln + 13lnx) + -1ln(x + -2) + -1ln(x + 1) = ln(12) + -1ln(x + -1) Reorder the terms: -11ln + 13lnx + -1ln(-2 + x) + -1ln(x + 1) = ln(12) + -1ln(x + -1) -11ln + 13lnx + (-2 * -1ln + x * -1ln) + -1ln(x + 1) = ln(12) + -1ln(x + -1) -11ln + 13lnx + (2ln + -1lnx) + -1ln(x + 1) = ln(12) + -1ln(x + -1) Reorder the terms: -11ln + 13lnx + 2ln + -1lnx + -1ln(1 + x) = ln(12) + -1ln(x + -1) -11ln + 13lnx + 2ln + -1lnx + (1 * -1ln + x * -1ln) = ln(12) + -1ln(x + -1) -11ln + 13lnx + 2ln + -1lnx + (-1ln + -1lnx) = ln(12) + -1ln(x + -1) Reorder the terms: -11ln + 2ln + -1ln + 13lnx + -1lnx + -1lnx = ln(12) + -1ln(x + -1) Combine like terms: -11ln + 2ln = -9ln -9ln + -1ln + 13lnx + -1lnx + -1lnx = ln(12) + -1ln(x + -1) Combine like terms: -9ln + -1ln = -10ln -10ln + 13lnx + -1lnx + -1lnx = ln(12) + -1ln(x + -1) Combine like terms: 13lnx + -1lnx = 12lnx -10ln + 12lnx + -1lnx = ln(12) + -1ln(x + -1) Combine like terms: 12lnx + -1lnx = 11lnx -10ln + 11lnx = ln(12) + -1ln(x + -1) Reorder the terms for easier multiplication: -10ln + 11lnx = 12ln + -1ln(x + -1) Reorder the terms: -10ln + 11lnx = 12ln + -1ln(-1 + x) -10ln + 11lnx = 12ln + (-1 * -1ln + x * -1ln) -10ln + 11lnx = 12ln + (1ln + -1lnx) Combine like terms: 12ln + 1ln = 13ln -10ln + 11lnx = 13ln + -1lnx Solving -10ln + 11lnx = 13ln + -1lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-13ln' to each side of the equation. -10ln + -13ln + 11lnx = 13ln + -13ln + -1lnx Combine like terms: -10ln + -13ln = -23ln -23ln + 11lnx = 13ln + -13ln + -1lnx Combine like terms: 13ln + -13ln = 0 -23ln + 11lnx = 0 + -1lnx -23ln + 11lnx = -1lnx Add 'lnx' to each side of the equation. -23ln + 11lnx + lnx = -1lnx + lnx Combine like terms: 11lnx + lnx = 12lnx -23ln + 12lnx = -1lnx + lnx Combine like terms: -1lnx + lnx = 0 -23ln + 12lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-23 + 12x) = 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 '(-23 + 12x)' equal to zero and attempt to solve: Simplifying -23 + 12x = 0 Solving -23 + 12x = 0 Move all terms containing l to the left, all other terms to the right. Add '23' to each side of the equation. -23 + 23 + 12x = 0 + 23 Combine like terms: -23 + 23 = 0 0 + 12x = 0 + 23 12x = 0 + 23 Combine like terms: 0 + 23 = 23 12x = 23 Add '-12x' to each side of the equation. 12x + -12x = 23 + -12x Combine like terms: 12x + -12x = 0 0 = 23 + -12x Simplifying 0 = 23 + -12x 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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