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Simplifying ln(x + -2) + -1ln(x + 11) = ln(x + -1) + -1ln(x + 15) Reorder the terms: ln(-2 + x) + -1ln(x + 11) = ln(x + -1) + -1ln(x + 15) (-2 * ln + x * ln) + -1ln(x + 11) = ln(x + -1) + -1ln(x + 15) (-2ln + lnx) + -1ln(x + 11) = ln(x + -1) + -1ln(x + 15) Reorder the terms: -2ln + lnx + -1ln(11 + x) = ln(x + -1) + -1ln(x + 15) -2ln + lnx + (11 * -1ln + x * -1ln) = ln(x + -1) + -1ln(x + 15) -2ln + lnx + (-11ln + -1lnx) = ln(x + -1) + -1ln(x + 15) Reorder the terms: -2ln + -11ln + lnx + -1lnx = ln(x + -1) + -1ln(x + 15) Combine like terms: -2ln + -11ln = -13ln -13ln + lnx + -1lnx = ln(x + -1) + -1ln(x + 15) Combine like terms: lnx + -1lnx = 0 -13ln + 0 = ln(x + -1) + -1ln(x + 15) -13ln = ln(x + -1) + -1ln(x + 15) Reorder the terms: -13ln = ln(-1 + x) + -1ln(x + 15) -13ln = (-1 * ln + x * ln) + -1ln(x + 15) -13ln = (-1ln + lnx) + -1ln(x + 15) Reorder the terms: -13ln = -1ln + lnx + -1ln(15 + x) -13ln = -1ln + lnx + (15 * -1ln + x * -1ln) -13ln = -1ln + lnx + (-15ln + -1lnx) Reorder the terms: -13ln = -1ln + -15ln + lnx + -1lnx Combine like terms: -1ln + -15ln = -16ln -13ln = -16ln + lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -13ln = -16ln + 0 -13ln = -16ln Solving -13ln = -16ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '16ln' to each side of the equation. -13ln + 16ln = -16ln + 16ln Combine like terms: -13ln + 16ln = 3ln 3ln = -16ln + 16ln Combine like terms: -16ln + 16ln = 0 3ln = 0 Divide each side by '3'. ln = 0 Simplifying ln = 0 The solution to this equation could not be determined.
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