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Simplifying ln(x + -3) + -1ln(x + 7) = ln(x + -2) + -1ln(x + 11) Reorder the terms: ln(-3 + x) + -1ln(x + 7) = ln(x + -2) + -1ln(x + 11) (-3 * ln + x * ln) + -1ln(x + 7) = ln(x + -2) + -1ln(x + 11) (-3ln + lnx) + -1ln(x + 7) = ln(x + -2) + -1ln(x + 11) Reorder the terms: -3ln + lnx + -1ln(7 + x) = ln(x + -2) + -1ln(x + 11) -3ln + lnx + (7 * -1ln + x * -1ln) = ln(x + -2) + -1ln(x + 11) -3ln + lnx + (-7ln + -1lnx) = ln(x + -2) + -1ln(x + 11) Reorder the terms: -3ln + -7ln + lnx + -1lnx = ln(x + -2) + -1ln(x + 11) Combine like terms: -3ln + -7ln = -10ln -10ln + lnx + -1lnx = ln(x + -2) + -1ln(x + 11) Combine like terms: lnx + -1lnx = 0 -10ln + 0 = ln(x + -2) + -1ln(x + 11) -10ln = ln(x + -2) + -1ln(x + 11) Reorder the terms: -10ln = ln(-2 + x) + -1ln(x + 11) -10ln = (-2 * ln + x * ln) + -1ln(x + 11) -10ln = (-2ln + lnx) + -1ln(x + 11) Reorder the terms: -10ln = -2ln + lnx + -1ln(11 + x) -10ln = -2ln + lnx + (11 * -1ln + x * -1ln) -10ln = -2ln + lnx + (-11ln + -1lnx) Reorder the terms: -10ln = -2ln + -11ln + lnx + -1lnx Combine like terms: -2ln + -11ln = -13ln -10ln = -13ln + lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -10ln = -13ln + 0 -10ln = -13ln Solving -10ln = -13ln 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 = -13ln + 13ln Combine like terms: -10ln + 13ln = 3ln 3ln = -13ln + 13ln Combine like terms: -13ln + 13ln = 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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