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Simplifying ln(11 + -5x) + -1ln(x + -2) = ln(x + -6) (11 * ln + -5x * ln) + -1ln(x + -2) = ln(x + -6) (11ln + -5lnx) + -1ln(x + -2) = ln(x + -6) Reorder the terms: 11ln + -5lnx + -1ln(-2 + x) = ln(x + -6) 11ln + -5lnx + (-2 * -1ln + x * -1ln) = ln(x + -6) 11ln + -5lnx + (2ln + -1lnx) = ln(x + -6) Reorder the terms: 11ln + 2ln + -5lnx + -1lnx = ln(x + -6) Combine like terms: 11ln + 2ln = 13ln 13ln + -5lnx + -1lnx = ln(x + -6) Combine like terms: -5lnx + -1lnx = -6lnx 13ln + -6lnx = ln(x + -6) Reorder the terms: 13ln + -6lnx = ln(-6 + x) 13ln + -6lnx = (-6 * ln + x * ln) 13ln + -6lnx = (-6ln + lnx) Solving 13ln + -6lnx = -6ln + lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '6ln' to each side of the equation. 13ln + 6ln + -6lnx = -6ln + 6ln + lnx Combine like terms: 13ln + 6ln = 19ln 19ln + -6lnx = -6ln + 6ln + lnx Combine like terms: -6ln + 6ln = 0 19ln + -6lnx = 0 + lnx 19ln + -6lnx = lnx Add '-1lnx' to each side of the equation. 19ln + -6lnx + -1lnx = lnx + -1lnx Combine like terms: -6lnx + -1lnx = -7lnx 19ln + -7lnx = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 19ln + -7lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(19 + -7x) = 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 '(19 + -7x)' equal to zero and attempt to solve: Simplifying 19 + -7x = 0 Solving 19 + -7x = 0 Move all terms containing l to the left, all other terms to the right. Add '-19' to each side of the equation. 19 + -19 + -7x = 0 + -19 Combine like terms: 19 + -19 = 0 0 + -7x = 0 + -19 -7x = 0 + -19 Combine like terms: 0 + -19 = -19 -7x = -19 Add '7x' to each side of the equation. -7x + 7x = -19 + 7x Combine like terms: -7x + 7x = 0 0 = -19 + 7x Simplifying 0 = -19 + 7x 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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