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Simplifying ln(x + -3) + -1ln(x + 5) = ln(x + -4) + -1ln(x + 2) Reorder the terms: ln(-3 + x) + -1ln(x + 5) = ln(x + -4) + -1ln(x + 2) (-3 * ln + x * ln) + -1ln(x + 5) = ln(x + -4) + -1ln(x + 2) (-3ln + lnx) + -1ln(x + 5) = ln(x + -4) + -1ln(x + 2) Reorder the terms: -3ln + lnx + -1ln(5 + x) = ln(x + -4) + -1ln(x + 2) -3ln + lnx + (5 * -1ln + x * -1ln) = ln(x + -4) + -1ln(x + 2) -3ln + lnx + (-5ln + -1lnx) = ln(x + -4) + -1ln(x + 2) Reorder the terms: -3ln + -5ln + lnx + -1lnx = ln(x + -4) + -1ln(x + 2) Combine like terms: -3ln + -5ln = -8ln -8ln + lnx + -1lnx = ln(x + -4) + -1ln(x + 2) Combine like terms: lnx + -1lnx = 0 -8ln + 0 = ln(x + -4) + -1ln(x + 2) -8ln = ln(x + -4) + -1ln(x + 2) Reorder the terms: -8ln = ln(-4 + x) + -1ln(x + 2) -8ln = (-4 * ln + x * ln) + -1ln(x + 2) -8ln = (-4ln + lnx) + -1ln(x + 2) Reorder the terms: -8ln = -4ln + lnx + -1ln(2 + x) -8ln = -4ln + lnx + (2 * -1ln + x * -1ln) -8ln = -4ln + lnx + (-2ln + -1lnx) Reorder the terms: -8ln = -4ln + -2ln + lnx + -1lnx Combine like terms: -4ln + -2ln = -6ln -8ln = -6ln + lnx + -1lnx Combine like terms: lnx + -1lnx = 0 -8ln = -6ln + 0 -8ln = -6ln Solving -8ln = -6ln 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. -8ln + 6ln = -6ln + 6ln Combine like terms: -8ln + 6ln = -2ln -2ln = -6ln + 6ln Combine like terms: -6ln + 6ln = 0 -2ln = 0 Divide each side by '-2'. ln = 0 Simplifying ln = 0 The solution to this equation could not be determined.
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